P  O-R.E  S  T 


UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


u 


FOREST  VALUATION 


BY 
HERMAN    HAUPT    CHAPMAN,    M.  F, 

Harriman  Professor  of  Forest  Management 
Yale  University  Forest  School 


FIRST  EDITION 

FIRST  THOUSAND 


NEW  YORK 

JOHN   WILEY   &    SONS,    INC. 
LONDON:  CHAPMAN  &  HALL,   LIMITED 


COPYRIGHT,  1914, 

BY 
HERMAN  HAUPT  CHAPMAN 


Stanbope  iprcas 

F.    H.GILSON   COMPANY 
BOSTON.  U.S.A. 


To 

HENRY  SOLON  GRAVES 

FORESTER 

IN  RECOGNITION   OF  THE   SERVICES  WHICH  HE  IS  RENDERING  TO   THE 
NATION  AND  TO  FORESTRY  BY  MAINTAINING  A  HIGH  STAND- 
ARD OF  EFFICIENCY  AND  INTEGRITY  IN  PUBLIC  OFFICE, 
AND    BY    UPHOLDING    BOTH    THE    SPIRIT    AND    THE 
LETTER   OF   NATIONAL   FOREST   POLICY 


:*54526 


PREFACE 


THE  term  Forest  Valuation,  applied  to  this  volume,  covers 
only  a  portion  of  the  subject  of  Forest  Finance,  which  is  usually 
separated  into  two  parts,  termed,  respectively,  Valuation  and 
Statics.  Valuation  deals  with  the  determination  of  the  value  of 
standing  timber,  both  mature  and  immature,  and  of  forest  soil, 
and  the  forest  as  a  whole.  Forest  Statics  deals  with  the 
comparison  of  financial  results  obtained  in  forestry  with  those 
yielded  by  other  enterprises,  and  compares  the  relative  merits 
of  different  methods  of  treating  the  forest.  This  subject  is  dis- 
cussed in  Chapter  VIII.  Since  Forest  Valuation  includes  the 
greater  portion  of  the  text,  and  this  term  is  more  familiar  to 
American  foresters,  it  has  been  adopted  as  the  title,  in  place  of 
the  more  comprehensive  term,  Forest  Finance. 

The  literature  of  Forest  Finance  is  largely  of  German  origin, 
and  has  been  developed  in  the  latter  half  of  the  nineteenth 
century,  by  numerous  German  and  French  authorities.  The 
standard  English  text  is  found  in  "Forest  Management,"  by 
Sir  William  Schlich,  Vol.  Ill,  Part  II,  Forest  Valuation.*  This 
author  follows  the  continental  treatment  of  the  subject.  In 
1909,  a  pamphlet  on  "  Forest  Finance  "  was  published  by  C.  A. 
Schenck,  Ph.D.,  Forester  to  the  Biltmore  estate,f  which  gives  a 
synopsis  or  outline  of  a  series  of  lectures  on  the  subject.  Dr. 
Schenck's  treatment  is  thoroughly  American  and  contains  valu- 
able suggestions  for  the  advanced  student  of  Forest  Finance. 

Unfortunately,  neither  of  these  publications  treats  the  subject 
in  a  sufficiently  elementary  manner  to  serve  as  a  textbook  for 
students  of  forestry  or  for  persons  desiring  information  who  are 
not  already  thoroughly  familiar  with  the  economic  and  mathe- 

*  Fourth  Edition,  Revised.  Bradbury,  Agnew  &  Co.,  Ld.,  10  Bouverie  St., 
London,  1911. 

t  Inland  Press,  Asheville,  N.  C.,  1909. 
v 


Vi  PREFACE 

matical  principles  on  which  the  theory  of  Forest  Finance  is 
based.  Forest  Valuation  deals  with  periods  of  time  far  longer 
than  are  considered  in  most  financial  calculations.  The  theory 
and  application  of  compound  interest  as  a  mathematical  means 
of  determining  value  needs  a  more  complete  exposition  than  is 
usually  given  even  in  courses  in  economics,  before  the  signifi- 
cance of  the  methods  taught  in  valuation  can  be  grasped.  Forest 
Valuation,  while  disguised  as  a  mathematical  science,  is  in  reality 
the  application  of  broad  economic  principles,  equally  serviceable 
in  the  determination  of  all  values. 

In  order  that  the  reader  who  is  not  thoroughly  grounded  in 
economics  may  readily  grasp  these  principles  as  applied  in 
actual  Forest  Valuation,  Chapters  I  to  IV  have  been  devoted 
to  a  summary  of  economic  subjects  and  tenets,  with  especial 
emphasis  on  interest.  The  ideas  set  forth  follow  the  mathematical 
methods  used  by  many  economists  and  expressed  by  Prof.  Irving 
Fisher  of  Yale  University.*  These  chapters  will  serve  the 
additional  purpose  of  stating  the  economic  basis  upon  which 
the  discussion  of  disputed  questions  in  the  text  is  made  to  rest, 
and  will  enable  students  who  disagree  with  any  of  these  funda- 
mental definitions  or  principles  to  substitute  those  of  other 
authorities  more  to  their  liking. 

To  the  general  reader  and  even  to  the  student,  the  use  of 
formulae  as  a  means  of  expressing  economic  relations  is  apt  to 
convey  the  impression  that  the  subject  is  a  difficult  one  to  grasp. 
The  effort  to  attach  the  proper  significance  to  symbols  must 
precede  that  required  to  reach  the  mathematical  solution.  The 
first  difficulty  is  lessened  by  the  consistent  use  of  symbols  to 
which  a  definite  meaning  is  attached.  An  entire  chapter  (V) 
has  been  devoted  to  an  explanation  of  the  derivation  of  the 
formulae  of  compound  interest.  A  further  difficulty  has  arisen 
in  the  past,  because  the  methods  of  treatment  of  the  subject  of 
Forest  Valuation  bore  no  relation  to,  and  were  apparently  wholly 
at  variance  with,  the  customs  and  principles  of  business  account- 
ing. An  effort  has  been  made  in  the  present  volume  to  indicate 

"Elementary  Principles  of  Economics."    The  Macmillan  Company,  New 
York,  July,  1912. 


PREFACE  Vli 

these  relations,  and  enable  accountants  and  business  men  to 
harmonize  the  methods  used  in  computing  cost  and  value  for 
forest  property,  with  the  forms  and  ideas  with  which  they  are 
familiar. 

Lastly,  the  emphasis  has  been  shifted  from  the  determination 
of  expectation  value  of  forest  soil,  so  conspicuous  a  feature  of 
European  Forest  Finance,  to  the  consideration  of  stumpage 
values,  sale  values,  damages,  and  other  subjects  of  greater  prac- 
tical interest  in  this  country. 

The  volume  is  intended  primarily  for  use  as  a  textbook. 
But  in  recognition  of  the  frequent  need  for  information  on  such 
subjects  as  damages,  stumpage  values  and  costs  of  forest  pro- 
duction, a  consistent  effort  has  been  made  to  treat  the  entire 
subject  in  a  manner  that  may  be  readily  grasped  by  the  average 
reader,  without  previous  preparation  or  study. 

No  problems  have  been  included  in  the  text.  These  should 
be  supplied  by  instructors  to  suit  the  local  economic  conditions. 
The  table  of  logarithms  has  been  included  for  convenience,  to 
enable  the  student  to  familiarize  himself  with  its  use  in  solving 
problems  of  valuation. 

Acknowledgment  is  made  to  Prof.  Fred  R.  Fairchild  of  Yale 
University  for  review  and  criticism  of  Chapter  X  on  Taxation, 
to  Mr.  J.  E.  Glass,  accountant  for  John  Wiley  &  Sons,  Inc., 
for  suggestions  regarding  forms  for  forestry  accounts  shown  in 
Chapter  VIII,  and  to  my  colleagues  on  the  faculty  of  the  Yale 
Forest  School  for  valuable  suggestions  and  assistance. 

HERMAN  H.  CHAPMAN. 

NEW  HAVEN,  CONN., 
October  22,  1914. 


CONTENTS 


CHAPTER  I 

VALUES 
ARTICLE  PAGE 

1.  Wealth  and  Property i 

2.  The  Standard  of  Value i 

3.  Prices 2 

4.  Values 2 

5.  Demand 2 

6.  Effort  or  Outlay 3 

7.  Ownership 3 

8.  Prices  of  Finished  Products 4 

9.  Prices  of  Raw  Materials  and  Natural  Resources 5 

10.  Future  Costs 5 

11.  The  Element  of  Time  in  Values 6 

12.  Capital 6 

13.  The  Capitalist ; 7 

14.  Interest 7 

15.  Discount 8 

16.  Compound  Interest  and  Discount 8 

17.  Sale  Value ^ 9 

18.  Appraised  Value 10 


CHAPTER  II 
OUTLAY  AND  INCOME 

19.  Proprietary  Accounts  versus  Specific  or  Valuation  Accounts n 

20.  Capital  Accounts n 

21.  Outlay  and  Income  Accounts 12 

22.  Investments  versus  Expenses 13 

23.  The  Relation  in  Time  between  Outlay  and  Income 14 

24.  The  Total  Investment 14 

25.  Cost  Accounts 16 

26.  Income 16 

27.  The  Economic  Opportunity 16 

28.  The  Business  Venture 17 

29.  Exchange 17 

30.  Disposition  of  Income 17 

31.  Returns  on  Capital 18 

ix 


CONTENTS 

PAGE 

99.  Silvicultural  Operations • 74 

100.  Protection  Expenses 74 

101.  Administrative  Expenses 75 

102.  Taxes  and  Insurance 7" 

103.  Interest  Charges 

104.  Classification  of  Costs  in  Forest  Production ?6 

105.  Calculation  of  Total  or  Final  Costs 77 

106.  Total  Cost  of  Investments  in  Standing  Timber 79 

107.  Costs  of  Forestry  Compared  with  Destructive  Lumbering 81 

108.  Cost  of  Many-aged  Forests 83 

109.  Cost  of  Producing  a  Normal  Forest 84 


CHAPTER  VII 
THE  VALUATION  OF  FORESTS 

no.  Valuation  Accounts  in  Forestry 85 

in.   Income  as  the  Basis  of  Value  of  Forests 85 

112.  Value  of  Forest  Property  for  Destructive  Lumbering 86 

113.  Value  of  Forest  Property  for  Continuous  Forest  Production 88 

114.  Value  of  a  Forest  of  Even  Age  Just  Previous  to  Cutting 89 

115.  Value  of  an  Even-aged  Forest  for  Any  Year 90 

1 16.  Value  of  Forest  Soil 92 

117.  Value  of  Many-aged  Forests  Producing  Regular  Income 96 

118.  Value  of  Many-aged  Forests  Producing  Irregular  Income 97 

119.  Value  of  Timber  Separate  from  Land .  . , 98 


CHAPTER  Vin 
FOREST  STATICS  — THE  BALANCE  SHEET  —  PROFITS 

120.  Determining  the  Profits  of  an  Investment 100 

121.  The  Rate  of  Interest  in  its  Relation  to  Profits 104 

122.  Profits  in  Destructive  Lumbering 105 

123.  Profits  on  a  Stand  of  Timber 106 

124.  Anticipated  Profits  on  Young  Timber 106 

125.  Profits  from  Continuous  Forest  Production 107 

126.  Anticipation  of  Continuous  Profits 107 

127.  Profits  Expressed  as  Soil  Values 108 

128.  Profits  Expressed  as  a  Ratio  of  Income  to  Capital no 

129.  Earning  Power  of  Capital  Invested  in  Forest  Production in 

130.  The  Relative  Importance  of  Profits  in  Private  versus  Public  Forestry.  115 

131.  Forms  for  Specific  Accounts  in  Forestry 117 

132.  Forms  for  Economic  Accounts  in  Forestry 119 


CONTENTS  xiii 


CHAPTER  IX 

THE  APPRAISAL  OF  DAMAGES 

ARTICLE  PAGE 

133.  Principles  Underlying  Appraisal  of  Damages 120 

134.  Elements  of  Damage  to  Forest  Property 122 

135.  Physical  Separation  of  Timber  from  Soil 122 

136.  Separation  of  Value  of  Timber  from  Value  of  Soil 123 

137.  A  Basis  of  Damages:  Cost  of  Replacement 126 

138.  A  Basis  of  Damages:  Sale  Value 128 

139.  A  Basis  of  Damages:  Expectation  or  Capital  Value 129 

140.  Damage  to  Merchantable  Timber 131 

141.  Damage  to  Immature  Timber:  Partial  Loss 132 

142.  Damage  to  Immature  Timber:  Total  Loss 133 

143.  Damage  to  Forest  Soil 135 

144.  Damage  to  Single  Trees 136 

145.  Damage  to  Many-aged  Stands 137 

146.  Damage  to  Watersheds 137 

147.  ./Esthetic  Values 138 

148.  Punitive  Damages 139 


CHAPTER  X 
FOREST  TAXATION 

149.  Sources  of  Revenue  from  which  to  pay  Taxes 141 

150.  Tax  on  Income 141 

151.  Tax  on  Value  of^Property 142 

152.  Taxable  Value  of  Property 143 

153.  Effect  of  Taxes  on  Property  Values 143 

154.  The  General  Property  Tax 144 

155.  The  Problem  of  Taxation  for  Timberlands 145 

156.  Distinction  between  Capital  and  Income  in  Timber  Property 145 

157.  The  Problem  of  Interest  in  Forest  Taxation 146 

158.  Effect  of  Present  Condition  of  Forest  upon  Choice  of  Methods  of 

Taxation 147 

159.  Scientific  Taxation:  Forest  Property  Tax - 149 

160.  Scientific  Taxation:  Forest  Land  Tax 150 

161.  Comparison  of  Taxes  on  Forest  Rent  versus  Soil  Rent 151 

162.  Scientific  Taxation:  Income  or  Products  Tax 152 

163.  Scientific  Taxation:  Combined  Capital  Tax  and  Income  Tax 154 

164.  Taxes  under  the  General  Property  Tax 155 

165.  Effect  of  the  General  Property  Tax  on  Forest  Production 158 

166.  Tax  Reform  for  Forest  Property 160 


xvi  CONTENTS 

ARTICLE  PAGE 

239.  Timber  as  an  "Agricultural"  Value  ...............................  230 

240.  Stump  Land  versus  Cleared  Land  .............  ...................  231 

241.  Cost  of  Clearing  Stump  Lands  ...................................  232 

242.  Sale  Value  of  Stump  Lands  ...................  ...................  232 

243.  Summary  of  Elements  of  Value  for  Forest  Land  ....................  233 

244.  Value  of  Young  Timber  as  a  Part  of  the  Value  of  Forest  Soil  ........  234 

245.  Sale  Value  of  Forest  Property  ....................................  235 

246.  Discrimination  against  Forest  Values  ..............................  236 

247.  Discrimination  in  Favor  of  Forest  Values  ..........................  236 

248.  Results,  when  Values  of  Bare  Land  are  Compared  ..................  237 

249.  Results,  when  Full  Value  of  Property  is  used  in  Comparison  .........  237 

250.  National  Forest  Policy  in  Land  Classification  ......................  238 

251.  Reciprocal  Values  in  Forestry  and  Agriculture  .....................  239 

Appendix  ......................................................  240 

Summary  of  Formulas  of  Compound  Interest  .......................  240 

Definitions  of  Symbols  ..........................................  241 

Summary  of  Formulae  in  Forest  Valuation  .........................  243 

Costs  .....................................................  243 

Values  ....................................................  244 

Profits  ....................................................  246 

Interest  Earned  ..................................  .  .........  246 

Damages  ..................................................  247 

Depreciation  ...............................................  247 

Geometric  Series  ...........................................  248 

Stumpage  Values  ...........................................  24g 

Compound  Interest  Tables: 

Explanation  ........................  2. 


Tables  of  Logarithms  of  Numbers 


265 


ERRATA. 

Page    51.    TABLE  III. 

For  "  profit  "  read  "  loss  ". 
For  "  loss  "  read  "  profit  ". 
Page  134.     Lines  12  and  13. 

For  "  this  value  is  (C'  +  £')  -  (C  +  E)  in  which  (C'  +  £')  repre- 
sents "  read  "  the  original  value  of  Sv  is  C'  —  C,  in  which  C'  represents  ". 
Last  h'ne. 

For  "  (C'  +  £')  "  read  "  the  item  ". 
Footnote. 

First  line,  for  "  the  "  read  "  an  ". 
Second  line,  for  "  endures  "  read  "  occurs  ". 
Third  line,  for  the  entire  expression 

"  (£'  -  £)  (i.op>>  -  i)  instead  of  £'  -  E  "  read 


i.ojfi 
Page  135. 

First  line, 

for  "  (C  +£)"  read  "C'-C 
Formula  Q?.    Change  to  read 


-  (S*  +  E)+  (C  -  C). 

Page  157.    Formula  Ilia. 

Instead  of  "  (E-i.o/*20  -£  +  £')  i.o^10  -  E"  +  E'"  etc."  read 
"  (E-i.o/>2°  -£+£')  i.o/^0  -  E'  +  E"  etc." 

Page  247.     For  formula  Oa  read 


XVI 

ARTICLE 


CONTENTS 


FOREST  VALUATION 


CHAPTER   I 
VALUES 

1.  Wealth  and  Property.  —  Wealth  is  defined  as  material 
objects  owned  by  human  beings.     Forest  wealth  consists  of 
forest  land  and  its  resources,  principally  trees,  but  including  all 
other  materials  such  as  forage  and  game. 

Property  is  the  right  represented  by  ownership,  and  not  the 
material  object  itself.  The  benefits  derived  from  wealth  make 
its  ownership  desirable.  The  right  to  enjoy  these  benefits  is 
indicated  by  the  term  property.  The  satisfactions  to  be  derived 
from  ownership  of  forest  property,  aside  from  the  pleasures  of 
sport  and  recreation,  take  the  form  of  money  income  from  the 
sale  of  forest  products. 

2.  The  Standard  of  Value.  —  Value  is  an  expression  of  the 
relative  desirability  of  different  forms  of  wealth  or  property  in 
terms  of  a  common  standard.    The  form  of  wealth  accepted 
as  this  standard  is  termed  money,  and  is  exchangeable  for  all 
other  kinds  of  wealth  or  property.     The  present  standard  in 
this  country  is  gold.    The  value  of  money  itself  can  only  be 
measured  by  its  purchasing  power,  which  means  its  relative 
desirability  compared  with  other  goods.     Changes  in  the  quan- 
tity and  rapidity  of  circulation  of  money  cause  its  purchasing 
power  or  value  to  fluctuate,  and  a  decline  in  value  of  money 
means  higher  prices  for  all  other  property.     Prices  in  the  im- 
mediate past  have  risen.    If  continued,  this  tendency  will  be 
a  conservative  factor  in  the  valuation  of  forests;  while  in  con- 
trast, such  property  as  long  term  bonds  will  tend  to  fall  in  value, 
because  it  is  redeemable  in  money. 


2  FOREST  VALUATION 

3.  Prices.  —  A  price,  when  expressed  in  terms  of  the  common 
standard  of  value,  is  the  amount  of  money  accepted  in  exchange 
for  a  unit  of  goods.     Until  the  actual  exchange  is  consummated 
the  price  is  not  definitely  established,  but  exists  merely  as  an 
appraisal  or  opinion  in  the  mind  of  the  prospective  buyer  or  the 
present  owner.     Prices  resulting  from  exchanges  are  agreements 
between  two  persons  as  to  the  value  of  a  unit  of  property. 
Market  prices  originate  in  centers  of  trade  and  form  the  basis 
of  numerous  transactions.     Prices  are  therefore  of  human  and 
mental  origin  and  are  established  by  economic  causes  which 
influence  the  opinions  of  the  majority  of  purchasers  and  sellers. 
While  in  the  main,  prices  move  in  response  to  supply  and  demand, 
yet  the  fluctuations  in  price  of  certain  forms  of  property,  such 
as  real  estate  and  stocks,  demonstrate  that  it  is  possible  to 
create  market  prices  either  higher  or  lower  than  circumstances 
justify,  by  influencing  general  or  public  opinion  through  opti- 
mism, misrepresentation,  or  concealment  of  facts. 

4.  Values.  —  Value  may  be  denned  as  the  price  of  a  given 
unit  of  wealth,  multiplied  by  the  quantity  or  number  of  units. 
Thus  the  value  of  a  given  quantity  of  cordwood  is  the  price  per 
cord  multiplied  by  the  number  of  cords  on  hand.     This  defini- 
tion holds  good  if  prices  are  accepted  as  the  final  standard  of 
value.     For  finished   products,  especially  staple  commodities, 
actual  prices  established  by  exchanges  may  be  taken  as  deter- 
mining value.     But  for  forms  of  goods  in  an  unfinished  state, 
or  for  productive  wealth,  such  as  land  or  growing  timber,  prices 
furnish  only  contributory  evidence  of  value,  which  in  many 
instances  is  entirely  misleading.     The  very  fact  that  prices  for 
finished  products  are  the  basis  of  value  indicates  that  the  value 
of  productive  property  must  be  derived  from  that  of  its  products. 
Ignorance  of  the  true  productiveness  of  property,  and  of  the 
mathematical  relation  between  this  income  and  the  value  of 
the  property,  is  the  principal  cause  of  divergence  between  current 
prices  and  true  value  for  such  forms  of  wealth  as  forest  lands 
and  young  timber. 

5.  Demand.  —  The  influences  which  determine  prices  are 
twofold,  corresponding  roughly  to  the  two  persons  concerned 


VALUES  3 

in  the  transfer.  Demand,  or  the  need  of  the  purchaser,  is 
weighed  against  outlay  or  effort  on  the  part  of  the  owner.  The 
necessities  and  desires  of  the  human  mind  and  body,  such  as 
food,  clothing  and  shelter,  create  the  demand  for  any  form  of 
material  wealth.  Civilized  society  differs  from  primitive  condi- 
tions by  the  greater  extent  and  complexity  of  its  needs.  Values 
are  thus  created  which  have  no  existence  among  savages.  This 
fact  is  strikingly  illustrated  by  the  history  of  the  timberlands 
belonging  to  Indian  tribes.  To  the  American  Indians  the  pine 
timber  was  of  no  value  whatever,  and  their  use  of  the  forest  was 
confined  to  its  game  and  fish,  the  destruction  of  which  they 
deeply  resented.  Title  to  much  of  this  forest  land  was  given 
to  various  tribes  by  the  government.  This  timber  soon  came 
to  have  a  high  value  to  the  white  population,  and  the  Indians 
were  either  defrauded  of  values  which  they  had  failed  to  appre- 
ciate, or  found  themselves  enriched  by  these  same  values  which 
they  had  no  part  in  creating. 

6.  Effort  or  Outlay.  —  Human  demand  or  needs  would  not 
alone  create  values.     Materials  indispensable   to  life    remain 
without  value  when  they  can  be  obtained  without  effort.     Prop- 
erty which  is  worth  owning  has  cost  the  original  owner  some 
effort  either  for  its  acquisition  or  improvement.    This  influences 
his  idea  of  its  value.    A  prospective  purchaser  gauges  his  price 
by  the  possibility  of  securing  a  similar  article  through  his  own 
efforts.    The  supply  of  finished  products  is  greatly  influenced 
by  cost  of  production. 

7.  Ownership.  —  The  whole  structure  of  values  rests  on  the 
institution  of  private  property,  for  without  the  right  of  owner- 
ship there  could  be  no  measurable  value.     In  a  primitive  state 
of  society  each  individual  is  able,  after  a  fashion,  to  supply  his 
own  needs.     But  with  specialization  and  division  of  labor,  pro- 
ducers of  most  forms  of  wealth  need  very  little  of  it  themselves 
and  must  sell  it,  while  the  purchasers  would  be  unable  to  produce 
for  themselves  the  small  quantities  they  need  at  anything  like  the 
price  at  which  it  is  sold.    Purchasers  therefore  seek  the  lowest 
price,  while  owners,  in  order  to  dispose  of  their  surplus  or  to  in- 
crease their  output,  often  underbid  one  another.    With  unlimited 


4  FOREST  VALUATION 

competition  among  producers,  prices  tend  frequently  to  fall 
below  the  cost  of  production.  But  where  the  supply  of  an 
article  of  wealth  is  limited,  and  no  satisfactory  substitutes  are 
available,  the  owner  may  demand  and  receive  exorbitant  prices, 
profiting  by  the  needs  of  the  consumers.  In  such  cases  there 
is  no  relation  between  prices  and  cost  of  production.  Famine 
prices  for  food  are  obtained  in  times  of  flood  or  temporary 
scarcity.  Elements  which  tend  to  increase  the  advantage  of 
the  owner  and  the  margin  between  costs  and  value  are:  first, 
absence  or  monopoly  of  transportation  facilities;  second,  the 
elimination  of  competition,  by  monopoly  of  the  sources  of  supply 
or  manufacture;  and  third,  monopoly  of  markets.  In  some 
lines  of  production  this  control,  through  the  power  incidental  to 
ownership,  has  curtailed  production  and  has  had  a  marked  effect 
upon  prices.  Combinations  or  trade  agreements  may  bring 
about  this  result.  This  condition  is  manifested  in  the  lumber 
trade  chiefly  by  the  maintenance  of  local  retail  prices  regard- 
less of  the  fluctuations  of  the  general  lumber  market.  Rail 
competition  will  prevent  the  possibility  of  combination  on 
the  part  of  manufacturers  of  lumber  for  an  indefinite 
period. 

8.  Prices  of  Finished  Products.  —  Since  the  immediate 
needs  of  persons  and  their  satisfaction  from  material  sources 
create  value,  it  follows  (§  4)  that  the  prices  established  for  goods 
ready  for  immediate  consumption  or  use  are  the  basis  or  source 
of  value  for  all  forms  of  wealth.  Both  needs  and  prices  are  a 
matter  of  to-day.  The  element  of  cost,  in  so  far  as  it  affects 
prices,  is  completed  in  the  final  product.  Purchasers  and  venders 
are  separated  into  two  classes  with  sharply  divided  interests, 
the  one  obliged  to  buy,  the  other  with  no  recourse  but  even- 
tually to  sell.  Under  such  circumstances  prices  absolutely 
determine  value.  The  price  of  lumber,  ties,  cordwood  and  other 
forest  products  depends  to  as  great  an  extent  upon  the  demand 
and  markets  as  upon  the  cost  of  production,  and  in  periods  of 
depression,  lumber  frequently  sells  for  less  than  this  cost.  But 
whatever  the  conditions,  these  market  prices  determine  the 
value  of  forest  products. 


VALUES  5 

9.  Prices  of  Raw  Materials  and  Natural  Resources.  —  Raw 

materials,  such  as  pig  iron  or  wool,  are  valuable  to  owner  or 
purchaser  only  for  further  manufacture.  A  lowering  of  the  cost 
of  production  makes  it  possible  to  sell  these  products  more 
cheaply,  but  scarcity  and  increased  demand  may  completely 
offset  this  tendency  and  cause  higher  prices.  The  value  of  raw 
products  is  derived  directly  from  the  price  of  finished  goods. 
Logs  and  timber  stumpage  derive  their  value  from  retail  and 
wholesale  lumber  prices.  Property  used  for  production  is  valu- 
able only  because  of  its  products.  The  value  of  agricultural 
land  depends  upon  its  adaptability  for  certain  kinds  of  farm 
crops,  and  upon  the  prices  these  crops  will  bring.  The  market 
price  for  lumber  is  the  source  of  value  for  forest  land. 

Prices  for  land  should  therefore  depend  entirely  upon  future 
income  derived  from  its  products  or  use.  Costs  already  incurred 
for  clearing  or  improvements  are  not  considered,  for  if  land  is 
worth  either  more  or  less  than  the  cost  of  clearing,  its  value 
and  not  its  cost  will  fix  its  price.  If  two  grades  of  land,  one 
good  and  one  poor,  cost  the  same  amount  for  clearing,  they 
will  still  sell  for  entirely  different  prices.  Both  the  owner  and 
the  purchaser  of  land  desire  it  merely  for  its  future  use  and 
income.  Sale  is  seldom  forced,  since  the  owner  can  probably 
make  a  living  by  developing  and  using  the  property.  The  price 
paid  for  such  property  thus  depends  upon  expected  income  whose 
value  is  determined  by  the  prices  of  the  products  which  the  land 
yields. 

10.  Future   Costs.  —  While  costs  already  incurred  do  not 
determine  the  value  of  productive  wealth,  future  costs  which 
intervene  between  the  present  moment  and  the  final  attainment 
of  income  must  be  subtracted  from  the  value  of  this  income. 
If  it  can'  be  shown  that  the  future  cost  of  obtaining  income 
exceeds  the  future  value  of  the  income,  the  property  itself  will 
be  worthless.     Thus  the  value  of  standing  timber  is  the  margin 
left  after  subtracting  from  the  sale  value  of  the  lumber  the  esti- 
mated costs  of  logging,  manufacturing  and  transporting  this 
lumber  to  market.     At  present  prices,  nearly  all  standing  timber 
has  a  stumpage  value,  but  in  the  past  only  the  most  accessible 


6  FOREST  VALUATION 

trees  had  any  value.  Wild  land  or  stump  land  may  be  worthless 
under  present  conditions,  in  spite  of  a  fertile  soil,  if  it  is  evident 
that  the  labor  of  clearing  exceeds  the  discounted  value  of  the 
income  from  the  crops  which  may  be  raised.  Most  land  is  cleared 
at  an  economic  loss,  and  there  is  a  tendency  to  hold  cut-over 
or  stump  lands  at  prices  which  greatly  exceed  their  real  value 
as  reduced  by  the  future  costs  of  clearing. 

11.  The  Element  of  Time  in  Values.  —  As  prices  and  values 
center  upon  the  satisfaction  of  human  needs  in  the  present 
moment,  the  tendency  is  to  avoid  delay  and  reduce  as  far  as 
possible  the  period  which  elapses  between  effort  and  satisfac- 
tion.   Yet  this  element  of  time  intervenes  in  every  process  of 
production.     Hunting  and  fishing  supply  food  within  a  very 
short  period,  which  explains  the  dependence  placed  upon  this 
source  of  living  by  primitive  people.     In  agriculture,  the  period 
which  must  elapse  between  effort  and  satisfaction  is  extended 
to  cover  the  crop  season,  and  enough  surplus  must  be  produced 
to  last  a  year.     Modern  engineering,  illustrated  by  railroad 
construction,  requires  still  greater  delay  before  any  use  or  income 
can  be  derived  from  the  property.     If  the  laborers  who  construct 
such  works  were  also  the  owners,  and  dependent  for  their  living 
upon   the   receipts   from   freight   and   passenger   service,    they 
would  starve  long  before  the  completion  of  the  road.     The 
development  of  civilization  is  marked  by  the  lengthening  of  the 
time  intervening  between  the  inception  of  undertakings  and 
the  final  realization  of  income.     This  time  element  must  always 
be  considered  in  the  determination  of  present  values. 

12.  Capital.  —  Men  must  live  while  engaged  in  production, 
and  they  are  enabled  to  undertake  enterprises  requiring  time, 
only  when  they  have  enough  goods  stored  up  to  last  them  until 
their  completion.     The  wealth  with  which  to  supply  them  con- 
sists of  food,  clothing  and  dwellings,  back  of  which  are  factories, 
raw  products  and  land.     The  amount  of  energy  that  can  be 
diverted  from  immediate  production  of  food  to  the  task  of 
clearing  unproductive  land  or  constructing  other  improvements 
depends  upon  the  surplus  wealth  available  for  these  purposes. 
A  poor  man  works  a  lifetime  to  clear  up  a  wooded  farm  and  at 


VALUES  7 

first  must  earn  wages  by  outside  labor  in  order  to  live.  But  a 
person  possessed  of  a  few  thousand  dollars  or  its  equivalent  can 
hire  this  work  done  and  accomplish  it  in  a  short  time. 

The  term  capital  is  used  to  signify  a  stock  of  wealth  existing 
at  a  given  instant  of  time,  and  therefore  available  for  future 
use.  All  wealth  is  capital.  Efforts  to  separate  wealth  into 
classes,  such  as  that  which  is  intended  for  consumption,  and  that 
used  for  the  production  of  other  wealth,  lead  to  confusion.  It 
is  immaterial  whether  a  man's  capital  is  in  the  form  of  food, 
buildings,  land  or  money.  He  will  endeavor  to  secure  by  ex- 
change a  proper  balance  between  the  different  kinds  of  capital 
he  possesses.  The  exchange  of  wheat  for  money,  its  reserva- 
tion for  seed  or  its  conversion  into  flour  does  not  alter  its  status 
as  capital. 

13.  The  Capitalist.  —  With  sufficient  capital  a  man  is  not 
only  free  from  immediate  personal  wants  but  by  employment 
and  the  payment  of  wages,  can  provide  for  the  daily  wants  of 
others.     On  this  basis  all  modern  business  enterprises  are  con- 
ducted.    The  time  needed  in  constructive  works  may  be  lessened 
by  increasing  the  number  of  persons  employed  and  the  capital 
expended,  but  only  to  a  limited  extent.     For  crop  production, 
and  in  the  growing  of  trees,  the  time  required  cannot  be  appre- 
ciably reduced.     Since  it  is  only  by  the  use  of  capital  that  any 
enterprise  requiring 'time  can  be  undertaken,  capitalists  make 
possible  the  entire  fabric  of  modern  civilization,  and  without 
this  accumulated  surplus  we  would  revert  to  primitive  condi- 
tions.    In  forest  production  the  element  of  time  is  so  important 
that  the  trend  is  toward  state  and  national  forestry,  for  govern- 
ments represent  the  accumulated  capital  of  the  entire  community 
and  can  best  afford  to  await  the  maturing  of  timber  crops  by 
the  slow  process  of  growth. 

14.  Interest.  —  The  present  moment  is  the  basis  for  comput- 
ing and  comparing  all  values.    Although  use  and  income,  on 
which   value   depends,   continue  into   the  future  indefinitely, 
yet  no  one  will  provide  for  future  wants  and  leave  present 
demands  wholly  unsatisfied.     To  every  one  the  enjoyment  of 
wealth  in  the  present  is  valued  more  highly  than  at  any  future 


8  FOREST  VALUATION 

period,  and  the  less  capital  a  man  has  the  greater  is  his  prefer- 
ence for  its  immediate  use.  This  preference  can  be  satisfied 
by  borrowing.  The  borrower  obtains  the  benefits  he  seeks 
immediately,  but  the  lender  is  forced  to  wait  until  the  capital 
is  returned  before  enjoying  it.  For  this  gain  in  "  time  value," 
the  borrower  pays  interest.  Upon  money  loans  interest  is 
repaid  in  money,  the  amount  paid  bearing  a  definite  relation 
to  the  amount  borrowed  and  to  the  length  of  time  elapsing 
before  repayment.  Since  interest  and  principal  are  in  the  same 
commodity,  money,  the  relative  amount  and  value  of  the  interest 
can  be  expressed  as  a  per  cent  of  the  principal.  This  per  cent 
gives  the  rate  of  interest  paid  or  earned.  The  period  for  which  this 
rate  is  customarily  quoted  is  one  year.  If  the  period  intended 
is  less  than  a  year  the  fact  must  be  clearly  stated.  High  rates 
of  interest  may  be  based  on  the  month,  in  order  to  make  the 
rate  sound  less  exorbitant. 

Interest,  therefore,  is  the  price  of  time  differences  or  the  stand- 
ard by  which  the  value  of  immediate  possession  and  enjoyment 
of  income  can  be  determined,  when  compared  with  the  value  of 
the  same  income  if  its  receipt  is  postponed  to  a  future  period. 

15.  Discount.  —  All  future  values  can  be  standardized  by 
reducing  them  to  their  equivalent  present  value  by  means  of 
a  given  rate  of  interest.     This  process  of  reduction  is  termed 
discount.     The  discounting  of  money  loans  or  demand  notes 
consists  of  receiving  in  advance  the  value  of  a  sum  receivable 
in  the  future,  less  the  difference  in  value  due  to  the  time  elapsing 
before  this  payment  is  due.     In  the  same  way  the  present  value 
of  all  forms  of  property  is  derived  by  consciously  or  uncon- 
sciously discounting  its  future  value  which  takes  the  form  of 
future  income.     The  process  of  discounting  is  therefore  the  most 
important  element  in  the  valuation  of  forest  property. 

16.  Compound  Interest  and  Discount.  —  Interest  upon  money 
loans  is  due  and  payable  either  annually  or  at  shorter  intervals. 
When  received  it  may  be  added  to  the  principal  at  the  discretion 
of  the  owner.     It  may  then  be  loaned  and  will  in  turn  earn 
interest.    At  the  end  of  each  period  of  payment,  provided  no 
capital  has  been  withdrawn,  and  interest  has  been  promptly 


VALUES  9 

reinvested,  the  total  investment  will  have  increased  by  an  amount 
representing  the  interest  on  the  total  sum  on  hand  at  the  begin- 
ning of  the  period.  A  sum  earning  interest  in  this  manner 
increases  at  a  compound  or  geometric  rate. 

Should  the  annual  interest  earned  be  withdrawn  annually, 
neither  the  principal  nor  the  interest  earned  would  increase  in 
amount.  Should  this  interest  be  saved  but  not  reinvested,  the 
total  value  of  principal  and  accumulated  interest  would  increase 
by  the  same  amount  annually.  This  is  termed  simple  interest. 
In  neither  of  these  cases  is  compound  interest  obtained.  Com- 
pound interest  is  paid  by  savings  banks  on  deposits  which  remain 
untouched  for  periods  of  six  months  or  more. 

Since  the  earning  of  interest  on  money,  without  expenditure 
or  withdrawal  of  the  earnings,  is  equivalent  to  depriving  the 
owner  of  this  capital  of  all  use  of  his  property  for  the  period 
covered  by  the  loan,  the  difference  in  value  of  the  capital  at 
the  beginning  and  end  of  the  period  measures  the  money  value 
of  the  period  of  waiting.  When  money  is  loaned  for  periods 
exceeding  one  year,  this  difference  in  value  must  be  computed 
by  compound  interest.  Any  lesser  sum  would  fall  short  of  the 
demonstrated  earning  power  of  money  capital  at  a  given  rate 
of  interest.  Since  compound  interest  is  thus  required  for  money 
loans  it  must  be  accepted  also  as  the  standard  of  time  differences 
in  value  for  all  other  forms  of  income. 

By  means  of  compound  interest  at  a  given  rate  the  exact 
ratio  is  obtained  by  which  present  values  may  be  converted 
into  future  values,  or,  by  discount,  future  values  may  be  re- 
duced to  their  present  equivalents.  When  both  the  present 
and  future  values  are  known,  a  rate  of  compound  interest  may 
be  found  which  will  equalize  the  difference  in  time  and  convert 
the  one  value  into  the  other. 

17.  Sale  Value.  —  The  sale  value  of  property  is  indicated 
by  recent  prices  for  similar  property  in  the  same  locality.  In 
the  absence  of  actual  sales  it  is  difficult  to  determine  present 
sale  value. 

Sale  values  are  not  uniform  for  the  same  kind  and  quality  of 
goods,  even  in  the  same  locality,  unless  there  is  a  complete 


10  FOREST  VALUATION 

general  knowledge  of  current  prices  and  the  desire  to  buy  is 
approximately  equal  to  the  pressure  for  sales.  Should  the  owner 
stand  in  need  of  money  he  will  tend  to  lower  prices,  and  vice 
versa.  Forced  sales  for  cash  or  to  liquidate  assets  are  made 
at  prices  much  below  the  market  and  establish  what  are  termed 
wrecking  values.  The  difference  in  value  due  to  forced  sales 
is  greatest  with  property  used  in  production  or  for  special  pur- 
poses, of  which  real  estate  is  a  good  example.  A  forced  sale 
of  forest  lands,  especially  of  young  timber  with  no  market  value, 
will  seldom  secure  more  than  a  fraction  of  the  true  value  of 
the  property. 

18.  Appraised  Value.  —  Values  must  frequently  be  estab- 
lished in  the  absence  of  sales,  or  as  a  basis  for  such  transactions 
when  previous  sales  are  either  lacking  or  unreliable  as  a  standard 
of  value.  Instances  are  found  in  condemnation  proceedings, 
in  settlements  for  damages,  and  in  inventories  or  the  valuation  of 
assets  for  purposes  of  determining  the  financial  status  of  a  busi- 
ness. The  principle  underlying  appraisals  is  that  the  value 
to  the  owner,  for  continued  ownership  and  use,  must  be  deter- 
mined rather  than  its  possible  value  for  sale,  since  the  owner 
must  not  be  forced  to  accept  a  lower  value  than  that  represented 
by  his  use  or  enjoyment  of  the  property.  Appraised  values,  for 
this  reason,  frequently  differ  sharply  from  sale  values,  especially 
in  the  case  of  slow-moving  assets. 


CHAPTER   II 
OUTLAY  AND  INCOME 

19.  Proprietary  Accounts  versus  Specific  or  Valuation  Ac- 
counts. —  Modern    accounting    distinguishes    two    classes    of 
accounts,  proprietary  accounts  and  specific  or  valuation  accounts. 
Proprietary  accounts  deal  with  the  proprietor  or  owner's  in- 
terest, and  show  what  his  outlay  has  been,  the  resulting  income 
already  received  and  the  balance  which  represents  net  capital. 
These  accounts  show  the  owner  as  creditor  of  a  business  venture, 
the  credit  representing  his  investments.     Expenses  are  debited 
and  income  or  profits  credited.     Such  accounts  normally  show 
a  credit  balance.    The  credit  items  are  the  plus  items  of  the 
account.    Dealing  as  it  does  entirely  with  outlay  and  income, 
it  records  only  actual  transactions  or  past  events. 

Specific  or  valuation  accounts  deal  with  the  assets  or  goods 
for  which  these  expenses  are  incurred,  and  from  which  the  income 
is  expected.  In  contrast  to  economic  accounts,  they  determine 
the  value  of  these  assets,  and  may  thus  introduce  elements 
derived  from  the  future  as  well  as  the  past  (§  9). 

20.  Capital   Accounts.  —  Outlay   or   expenditure   of   capital 
is  undertaken  for  one  of  two  purposes.     Either  an  exchange 
is  effected  by  which  the  proprietor  receives  goods  or  property 
of  equal  value,  or  the  outlay  is  in  return  for  services  and  the 
equivalent  in  value  must  be  sought  in  the  effect  or  results  of 
such  services. 

In  accounting,  these  two  classes  of  outlay  are  rigidly  sepa- 
rated wherever  it  is  possible  to  do  so.  The  cost  of  tangible  assets, 
especially  of  those  which  have  a  more  or  less  durable  character 
and  permanent  value,  is  entered  in  a  capital  account.  This 
account  is  corrected  by  entering  deductions  from  cost  for  forms 
of  capital  which  depreciate  in  value  and  may  finally  become 
worthless.  This  factor  of  depreciation  is  common  to  all  forms 


I2  FOREST  VALUATION 

of  property  constructed  by  human  labor,  as,  for  example,  ma- 
chinery and  buildings.  The  charging  off  of  depreciation,  unless 
accompanied  by  an  appropriation  of  income  to  replace  the  capital 
originally  expended,  corresponds  to  a  loss  of  capital.  If  re- 
placed from  income,  it  serves  to  diminish  the  net  income  avail- 
able for  dividends.  In  either  case  it  improves  the  accuracy  of 
the  capital  account. 

A  capital  account  ought  to  show  at  any  time  the  total  amount 
of  capital  invested  in  permanent  or  durable  assets,  or  the  actual 
cost  of  these  assets,  whether  or  not  there  has  been  any  sub- 
sequent increase  in  value.  The  correction  for  depreciation, 
which  is  justified  by  the  fact  of  diminishing  value,  is  in  itself 
purely  a  matter  of  accounting.  The  amount  of  depreciation 
written  off  on  the  books  may  not,  and  usually  does  not,  coincide 
exactly  with  the  actual  loss  in  value  at  the  time.  Should  no 
account  be  taken  of  depreciation,  the  capital  account  would 
merely  show  that  the  owner  had  neglected  to  reduce  the  "  value  " 
or  appropriate  any  of  his  income  as  replacement  of  capital  cost. 
This  is  an  unwise  and  dangerous  practice,  but  it  is  optional 
with  the  owner  except  where  provision  for  depreciation  is  pre- 
scribed by  law  for  the  protection  of  stockholders  in  order  to 
bring  the  capital  account  into  closer  agreement  with  the  actual 
value  of  the  assets. 

21.  Outlay  and  Income  Accounts.  —  Outlay  and  income  ac- 
counts, more  often  termed  profit  and  loss  accounts,  deal  first 
with  the  expenditures  for  which  services  are  received  and  which 
are  not  therefore  chargeable  to  capital  account  or  regarded 
as  investments.  A  second  class  of  expenses  usually  included 
in  this  account  is  the  cost  of  raw  materials  to  be  manufactured, 
goods  to  be  resold,  supplies  to  be  expended  in  service,  and  fuel. 
These  items  represent  capital  and  their  value  will  be  included 
in  an  inventory.  But  in  most  forms  of  business  this  investment 
is  transitory  in  character,  the  raw  materials  are  turned  over  as 
quickly  as  possible,  and  the  resultant  income  is  expected  to  more 
than  cancel  these  outlays  during  the  current  year. 

Outlay  and  income  accounts  are  for  this  reason  kept  as  open 
accounts,  to  be  balanced,  usually,  at  annual  intervals.  Outlay 


OUTLAY  AND  INCOME  13 

is  debited  under  such  heads  as  wages,  transportation,  fuel,  in- 
surance, light,  rent,  repairs,  interest,  taxes,  supplies  and  cost  of 
raw  materials  or  goods.  Income  is  credited,  and  in  mercantile 
business  consists  almost  wholly  of  receipts  from  sale  of  goods, 
to  which  is  added  incidental  receipts  from  all  other  sources, 
such  as  rent  and  interest.  The  capital  account,  kept  separate 
from  this  mass  of  fluctuating  items  of  expense  and  income, 
is  brought  up  to  date  each  year  by  entering  against  it  the  net 
increase  or  decrease  in  actual  capital  resulting  from  the  trans- 
actions of  the  year.  Should  any  of  the  assets  whose  cost  is 
included  in  the  capital  account  be  sold,  the  income  thus  re- 
ceived must  be  credited  in  the  capital  account  to  replace  the  cost 
of  this  asset.  In  the  same  manner,  loss  in  value  of  capital  is 
replaced  through  the  depreciation  account.  Excess  of  sale  value 
over  cost  of  assets  would  be  credited  as  profits. 

22.  Investments  versus  Expenses.  —  The  distinctions,  or 
classifications  in  accounts,  adopted  by  experience  as  suitable 
for  modern  business  conducted  on  the  basis  of  annual  returns, 
should  not  be  allowed  to  conceal  the  economic  similarity  of 
all  forms  of  outlay  and  income.  Outlay  is  undertaken  with 
the  sole  purpose  of  thereby  securing  income.  Those  forms  of 
outlay  customarily  entered  in  the  capital  account,  for  which 
tangible  assets  are  received,  are,  it  is  true,  regarded  in  the  light 
of  investments  rather  than  expense  by  the  owner.  But  their 
acquisition  is  merely  the  first  step  in  securing  income,  and  the 
culmination  of  the  process  is  certain  to  require  services  or  labor. 
The  income  will  be  the  result  of  both  classes  of  expenditure. 
That  these  are  really  identical  is  seen  by  the  fact  that  improved 
property,  purchased  as  capital,  is  largely  the  result  of  the  ser- 
vices of  former  owners.  The  further  expenditure  for  services 
by  the  new  owner  may  have  a  sale  value  which  a  future  pur- 
chaser would  enter  not  as  expense  but  as  capital.  Expenses  for 
all  kinds  of  service  and  supplies,  instead  of  being  an  economic 
loss  as  must  of  necessity  be  assumed  in  the  practice  of  account- 
ing, is  the  most  important  form  of  investment,  without  which 
there  could  be  practically  no  income,  and  the  capital  would 
then  be  without  value.  The  controlling  purpose  of  the  pro- 


I4  FOREST  VALUATION 

prietor  is  to  obtain  as  great  a  ratio  of  income  as  possible  for  each 
unit  of  capital  employed,  whether  this  outlay  takes  the  form  of 
investment  or  subsequent  expenses. 

23.  The  Relation  in  Time  between  Outlay  and  Income.  - 
The  element  of  time  enters  into  every  process  of  production 
(§  n).    Effort  normally  precedes  satisfaction.    Money  income  is 
to  business  what  the  satisfaction  of  personal  wants  is  to  an  in- 
dividual.    Since  outlay  and  effort  are  synonymous,  it  follows 
that  in  all  forms  of  business,  investment  must  precede  the  re- 
ceipt of  income. 

This  process  is  easily  recognized  in  the  period  of  installation, 
especially  in  such  forms  of  business  as  require  the  completion 
of  material  structures.  But  it  is  equally  true  of  the  current 
business  of  a  going  concern.  The  receipt  of  income  is  reck- 
oned from  the  moment  a  trade  is  concluded.  Actual  payment 
may  be  delayed,  but  this  is  a  matter  of  accounting.  Upon  the 
delivery  of  the  goods,  all  expense  connected  with  the  securing 
of  this  income  terminates,  except  where  contracts  stipulate 
future  maintenance  in  good  order  for  a  stated  period.  Conse- 
quently, the  wages  and  all  other  charges  incurred  in  the  securing 
of  this  income  normally  precede  the  final  sale.  The  postpone- 
ment of  payment  of  these  expenses  is  also  a  mere  matter  of 
accounting.  The  liability  or  indebtedness  for  expenses  is  in- 
curred previous  to  receipt  of  income  in  practically  every  case. 

24.  The  Total  Investment.  —  The  total  capital  invested  in 
a  business  is  always  greater  than  that  represented  by  the  cost 
of  the  assets  listed  under  the  capital  account.     Were  income  and 
the  items  charged  under  expense  to  occur  simultaneously,  the 
one  should  cancel  the  other,  leaving  the  surplus  or  profit  to 
apply  as  interest  or  dividends  on  the  capital  originally  invested. 
After  a  business  is  established,  this  actually  takes  place  and  unless 
the  scope  of  operations  is  enlarged,  the  capital  required  should 
not  subsequently  increase.    But  this  apparent  coincidence  of 
income  and  outlay  does  not  alter  the  tune  relation  shown  to 
exist  between  them.    The  expenditures  of  to-day  are  for  the  pur- 
pose of  securing  future  income,  while  the  income  of  to-day  is  the 
result  of  past  outlays. 


OUTLAY  AND   INCOME  15 

These  outlays,  whether  in  form  of  services  or  purchases,  must 
be  paid  for  by  the  proprietor  at  the  time  they  are  incurred, 
either  in  money  or  credit.  This  evidently  requires  an  addition 
to  the  total  capital  invested,  sufficient  to  meet  all  expenses 
covering  the  period  of  installation  or  formation  of  the  business, 
or  the  time  elapsing  between  outlay  and  income.  If  the  income 
is  regular  and  continuous,  this  required  capital  ceases  to  increase 
as  soon  as  current  income  exceeds  current  outlay.  But  the  sum 
invested  up  to  this  point  remains  in  the  business,  for  whatever 
portion  may  be  paid  back  out  of  income  an  equal  sum  is  at 
once  required  to  meet  the  expenses  for  which  the  corresponding 
future  income  has  not  yet  materialized. 

The  capital  required  to  meet  these  current  expenses  and  carry 
them  continuously,  thus  bridging  the  gap  between  outlay  and 
income,  is  termed  working  or  floating  capital,  in  contrast  to 
that  represented  by  more  durable  assets  shown  in  the  capital 
account. 

For  business  in  which  income  is  realized  only  at  long  intervals, 
expenses  continue  during  the  period,  and  the  amount  of  working 
capital  tied  up  in  wages  and  supplies  increases  rapidly  to  large 
proportions,  and  is  as  suddenly  decreased  when  the  income  is 
received.  Such  a  condition  is  represented  by  the  business 
of  driving  logs  down  streams.  Contractors  engaged  in  this 
work  receive  their  settlement  when  the  logs  reach  their  desti- 
nation, which  is  once  a  year,  while  frequently  a  drive  is  hung 
up  and  lays  over  a  season.  It  was  formerly  the  custom  in  some 
states  to  transfer  this  indebtedness  or  outlay  to  the  shoulders 
of  the  laborers,  who  were  paid  in  time  checks  made  payable 
in  cash  at  a  date  subsequent  to  the  probable  delivery  of  the 
drive.  The  men,  being  without  capital,  cashed  these  checks 
at  discounts  which  allowed  the  bankers  or  speculators  who 
furnished  the  funds  to  make  very  large  profits.  These  profits 
were  in  some  cases  split  with  the  contractor  who  issued  the  checks. 
Legislation  has  in  most  instances  required  cash  payment  of 
wages,  thus  requiring  the  contractor  to  assume  this  obligation 
and  raise  the  necessary  working  capital.  Where,  as  in  the  case 
of  forest  plantations,  the  period  elapsing  between  outlay  and 


j6  FOREST  VALUATION 

income  becomes  abnormally  long,  the  amount  of  capital  required 
to  carry  the  project  to  completion  is  proportionally  increased. 

25.  Cost  Accounts.  —  A  cost  account  differs  from  a  general 
profit  and  loss  account  in  that  it  analyzes  the  cost  of  producing 
a  given  unit  of  output,  instead  of  accounting  for  the  current 
outlay  and  income  of  the  business  as  a  whole.     Such  an  account 
traces  the  history  of  the  product  from  the  time  of  its  purchase 
or  inception  until  it  is  sold.     The  costs  incurred  fall  into  two 
groups:    specific  costs,  which  include  that  for  raw  materials 
and  labor  directly  applied  in  production;   and  overhead  charges, 
which   include   taxes,   insurance,   light,    fuel,    superintendence, 
rent  and  other  items,  which  must  be  apportioned  on  an  equitable 
basis  over  the  entire  output.     Cost  accounts  in  forest  production 
sum  up  the  cost  of  growing  a  crop  of  timber  from  origin  to  matu- 
rity.    Owing  to  the  great  length  of  the  period  involved,  the 
factor  of  compound  interest  on  invested  funds,  when  introduced 
as  a  cost  in  such  accounts,  becomes  one  of  the  largest  items  of 
expense. 

26.  Income.  —  In  §  8  and  §  9  it  appears  that  prices  for  fin- 
ished products  are  the  source  of  value  for  all  forms  of  property. 
Value,  as  distinguished  from  cost,  depends  upon  net  income  and 
looks  to  the  future.     The  income  from  finished  products,  which 
gives  them  their  value,  corresponds  with  the  services  they  are 
capable  of  rendering  by  being  used  or  consumed. 

The  sources  of  income  from  productive  property  consist 
either  of  finished  products  or  materials  in  a  raw  or  unfinished 
state,  while  the  income  derived  from  the  business  of  operating 
such  properties  is  the  money  received  from  the  sale  of  the  output. 

27.  The    Economic    Opportunity.  —  To    derive    or    produce 
an  income,  some  human  want  must  be  supplied.     The  greater 
the  range  and  diversity  of  these  wants  and  the  greater  the 
purchasing   power  or   capacity  of   the   average   individual    to 
gratify  them,  the  more  numerous  and  promising  will  be  the 
economic  opportunities  for  business.     Inequalities  in  the  dis- 
tribution of  wealth,  and  the  existence  of  a  pauper  class,  greatly 
diminish  the  total  business  of  a  nation  and  divert  much  of  it 
into  wasteful  and  injurious  channels. 


OUTLAY  AND  INCOME  17 

28.  The  Business  Venture.  —  Income  can  be  produced  only 
by  risking  capital  and  expending  effort  on  the  chance  that  this 
outlay  will  be  returned  "with  interest."     In  a  properly  con- 
ducted business  this  risk  is  assumed  by  the  proprietor,  who 
makes   himself   personally    responsible    for    the    management. 
Ownership  is  represented  in  modern  business  by  capital  stock. 
By  means  of  this  same  device,  extensive  frauds  are  possible  by 
which  the  real  managers  of  a  business  shift  both  risk  and  loss 
to  the  stockholders  or  owners.    Legitimate  risk,  borne  by  those 
responsible  for  the  results,  is  unavoidable  and  is  one  of  the 
chief  characteristics  of  the  business  venture.    Aside  from  the 
risk  of  accidental  losses  by  fire,  theft  and  other  factors,  the  final 
ever-present  risk  is  that  income  will  be  insufficient  to  offset  the 
required  outlay,  and  insolvency  result. 

29.  Exchange.  —  Income    from   business    (§  26)    is    derived 
almost   entirely   from   sales   of  merchandise   or  manufactured 
products,  which  constitute  an  exchange  of  goods  for  money. 
The  transaction  is  in  theory  completed  with  the  delivery  of  the 
goods,  but  payment  is  often  deferred  and  constitutes  a  debt 
on  the  part  of  the  purchaser,  which  is  a  debit  or  asset  to  the 
business.    The  losses  which  occur  through  ultimate  failure  of 
debtors  to  pay  are  finally  debited  as  an  expense. 

30.  Disposition  of  Income.  —  With  the  receipt  of  income 
the  cycle  of  effort  is  completed  and  the  purposes  of  the  business 
are  accomplished.     An  accounting  must  now  be  rendered  to 
the  owner.     In  case  the  proprietor's  account  and  ownership  is 
terminated  by  a  sale  of  the  entire  business,  the  settlement  would 
consist  of: 

Payment  of  outstanding  bills,  wages  and  other  outside  obli- 
gations. 

Return  of  outstanding  and  borrowed  capital. 
Distribution  of  surplus  as  profit  to  owners  of  the  capital 

invested. 

In  the  annual  accounting  of  a  going  concern  the  profit  and 
loss  account  takes  care  of  the  expenses.  The  surplus  or  deficit 
in  annual  income,  shown  as  profit  or  loss,  is  carried  into  the 
annual  balance  sheet  for  future  disposal. 


l8  FOREST  VALUATION 

31.  Returns  on  Capital.  —  Out  of  the  net  profits  after  can- 
celling the  expenses  for  the  year,  provision  must  first  be  made  for 
the  replacement  of  capital  assets  lost  by  depreciation  or  other- 
wise.    The  remainder  is  available  as  returns  on  capital. 

Here  a  sharp  distinction  must  be  made  between  the  total 
amount  of  capital  required  to  finance  a  venture  and  the  persons 
or  sources  from  which  this  capital  is  derived.  From  the  stand- 
point of  the  business  itself,  the  source  or  ownership  of  this 
capital  has  no  effect  upon  the  total  net  profits  but  affects  merely 
the  apportioning  of  these  profits. 

A  proprietor  who  furnishes  his  entire  capital,  both  fixed  and 
working,  takes  all  the  profits  and  assumes  the  risk  of  loss.  But 
it  is  an  almost  universal  custom  to  borrow  part  of  the  needed 
capital  on  the  security  of  the  business  or  of  the  fixed  assets. 
In  this  case  profits  are  earned  on  the  total  invested  capital  as 
before,  but  the  division  is  on  a  different  basis.  The  borrowed 
capital  receives  a  fixed  rate,  agreed  upon  at  the  time  of  secur- 
ing the  loan,  and  guaranteed  by  the  proprietor.  He  receives 
in  turn  the  entire  surplus  remaining  after  this  obligation  is 
met. 

32.  Interest  versus  Dividends.  —  The   sum   guaranteed   to 
the  lender  of  borrowed  capital  is  interest.     This  is  paid  out  of 
net  income  and  is  as  much  a  part  of  the  net  earnings  of  the  busi- 
ness as  the  remainder.     The  residue  is  either  left  in  the  business 
as  additional  capital,  or  paid  to  the  proprietors  as  dividends. 

Interest,  at  the  rate  demanded  on  borrowed  funds,  will  require 
a  given  sum  on  the  entire  capital.  Should  the  business  earn  a 
net  income  exceeding  this  sum,  the  proprietor  receives  the  excess, 
which  raises  the  rate  earned  by  his  own  capital,  or  his  dividends, 
above  the  rate  of  interest  paid  to  creditors.  The  greater  the 
proportion  of  capital  he  borrows,  the  greater  will  be  the  rate  of 
dividends  on  the  lessened  capital  of  the  proprietor.  But  on 
failure  of  the  business  to  earn  the  rate  paid  on  borrowed  funds, 
the  owner  bears  the  entire  loss,  and  the  smaller  the  proportion 
which  his  capital  bears  to  the  whole  investment,  the  greater  is 
his  relative  loss. 

In  an  insolvent  concern,  the  owner's  capital,  as  well  as  divi- 


OUTLAY  AND  INCOME  19 

dends,  is  sacrificed  before  any  loss  of  either  interest  or  capital 
is  permitted  to  fall  upon  the  holder  of  mortgages  or  liens.  For 
this  reason  bankrupts  may  fraudulently  conceal  the  assets  and 
thus  defraud  creditors. 

33.  Profits.  —  According   to   Marshall,*   "  When   a  man  is 
engaged  in  business  his  profits  for  the  year  are  the  excess  of  his 
receipts  from  his  business  during  the  year  over  his  outlay  for 
his  business.    The  difference  between  the  value  of  his  stock 
and  plant  at  the  end  and  at  the  beginning  of  the  year  is  taken 
as  part  of  his  receipts,  or  as  part  of  his  outlay,  according  as 
there  has  been  an  increase  or  decrease  of  value.    What  remains 
of  his  profits  after  deducting  interest  on  his  capital  at  the  current 
rate  may  be  called  his  earnings  of  undertaking  or  management." 
According  to  this  definition,  interest  paid  on  borrowed  money 
is  excluded  from  profits,  but  interest  on  the  owner's  capital  is 
considered  as  constituting  part  of  the  profits.     This  is  the  dis- 
tinguishing point  between  a  purely  economic  or  impersonal 
consideration  of  a  business  and  a  personal  account  with  the 
proprietor.     In  an  economic  consideration  of  the  general  ques- 
tion of  profits  on  an  industry  as  a  whole,  such  as  is  needed,  for 
instance,  in  the  process  of  appraising  stumpage  values  for  stand- 
ing timber  (Chapter  XI),  the  distribution  of  the  required  capital 
between  proprietors   and   creditors  has   no   significance.     The 
entire  net  revenue  available  as  returns  on  capital  for  the  current 
year  must  be  regarded  as  profits. 

34.  Wages  versus   Profits.  —  Wages  are  an  outlay,  or  an 
expense,  which  serves  to  diminish  profits.     The  wage  or  salary, 
ultimately  met  from  income,  is  the  share  of  the  wage  earner 
in  the  returns  of  the  enterprise. 

In  most  undertakings  the  owners  themselves  give  at  least 
part  of  their  time  to  the  management  of  the  business.  In  very 
small  enterprises  the  owner  may  even  do  most  of  his  own  work, 
thus  saving  the  expense  of  employing  labor.  The  larger  forms 
of  business,  in  which  the  ownership  is  scattered  in  the  form  of 
capital  stock,  are  managed  by  proxy,  through  boards  of  direc- 

*  "Principles  of  Economics,"  by  Alfred  Marshall,  5th  Ed.,  Vol.  I,  p.  142. 
Macmillan  &  Co.,  London,  1907. 


20  FOREST  VALUATION 

tors  who  devote  but  a  small  portion  of  their  time  to  these  duties. 
There  is  an  almost  complete  separation  between  wages  or  salaries, 
and  income  in  the  form  of  dividends.  Even  in  such  cases, 
capable  managers  are  frequently  given  an  interest  in  the  business 
and  their  returns  thus  include  both  wages  and  dividends,  although 
the  two  items  are  separately  accounted  for.  In  small  ventures 
managed  by  the  owner,  this  distinction  is  often  neglected,  and 
the  owner's  profits  are  the  sole  source  of  compensation  for  his 
time.  In  such  cases  a  sum  representing  the  wages  of  the  manager 
or  overseer  should  be  charged  to  expense.  Should  the  business 
pay  less  than  this  sum  it  is  unprofitable. 


CHAPTER  III 
INTEREST 

35.  The   Problem   of   Interest.  —  In   proprietary   accounts, 
all  items,  with  the  exception  of  interest,  are  easily  classified  as 
costs  or  as  income.     Interest  may  be  regarded  as  either  cost 
or  income,  according  to  the  point  of  view.     Since  these  two 
conceptions  are  not  interchangeable,  a  clear  understanding  of 
this  problem  is  necessary  to  avoid  errors  in  dealing  with  ques- 
tions of  valuation  accounting. 

36.  Interest  as  a  Cost.  —  Interest  when  regarded  as  a  cost 
must  be  considered  in  its  relation,  first  to  the  owners  of  capital, 
and  second,  to  the  capital  itself.     In  accounting,  the  interest 
paid  upon  borrowed  capital  is  regarded  by  the  proprietors  as  a 
cost.     But  it  must  be  noted  that  the  net  profits  of  the  business 
are  first  computed,  and  from  these  profits,  rather  than  from 
gross  income,  the  cost  of  interest  is  met  (§32).     This  item  of 
cost  is  entirely  a  personal  matter  between  the  owner  and  his 
creditors.     Should  there  be  no  borrowed  capital,  this  cost  item 
would  disappear  from  the  account,  and  dividends  or  additions 
to  surplus,  to  an  equal  amount,  would  be  substituted. 

But  since  borrowed  capital  is  entitled  to  receive  interest  at  a 
standard  rate,  and  this  "cost"  must  be  met,  the  owner  con- 
siders that  his  own  capital  is  entitled  to  receive  interest  at  a 
like  rate.  He  guarantees  payment  on  loans,  but  must  depend 
on  his  own  exertions  to  obtain  this  interest  on  both  the  borrowed 
funds  and  on  his  own  investment.  Should  he  prefer  the  role  of 
money  lender,  his  capital  will  earn  this  rate  of  interest  without 
the  risks  attendant  on  the  business  venture.  The  risks  of  lending 
money  upon  good  security  are  much  less  than  those  accom- 
panying other  forms  of  business.  Shall  he  therefore  charge 
interest  upon  his  entire  capital  as  a  cost  which  must  be  met? 
Those  who  take  this  view  will  include  interest,  not  only  on 


22  FOREST  VALUATION 

borrowed  funds  but  on  the  total  invested  capital,  in  the  same 
category  as  other  expenses,  that  is,  as  a  part  of  the  so-called 
carrying  charges  of  the  business. 

The  interest  to  which  the  owner  is  entitled  cannot  be  entered 
in  proprietary  accounts  as  an  actual  charge  or  cost  similar  to 
interest  on  borrowed  funds.  His  share  of  interest  is  never 
actually  expended,  and  the  idea  of  cost  exists  merely  by  impli- 
cation. But  in  a  cost  account,  which  is  intended  to  present 
definitely  the  relation  between  total  cost  of  production  and 
resulting  income,  interest  may  be  calculated  and  entered  as  a 
part  of  the  total  cost. 

37.  Interest  as  Income.  —  Whether  or  not  interest  is   re- 
garded as  a  cost,  it  always  represents  income  on  the  capital 
investment,  and  in  this  respect  differs  from  other  costs.     All 
other  items  of  expense,  such  as  taxes,  wages  and  cost  of  supplies, 
while  met  eventually  from  income,  go  to  persons  or  enterprises 
other  than  the  capitalists  who  finance  the  venture.     And  just 
as  the  creditors  of  the  business,  during  the  formative  period, 
are  paid  in  advance  by  the  capitalist,  who  receives  returns 
finally  from  income,  so  the  capitalist  who  only  loans  money  and 
does  not  assume  the  risks  of  ownership  may  receive  his  interest 
in  advance  of  income,  provided  it  falls  due  and  is  paid  by  the 
proprietor.     But  this  cost  to  the  latter  is  ultimately  returned  to 
him  from  income,  which  must  also  pay  him  returns  on  his  own 
investment.     In  case  the  income  is  continuous  and  is  accounted 
for  annually,  both  borrowed  and  invested  capital  receive  income 
directly  from  the  net  returns. 

38.  The  "Rate  of  Interest."  —  Interest  has  been  denned  as 
the  price  of  time  differences  in  the  enjoyment  of  income  (§14). 
Since  the  use  or  borrowing  of  capital  is  the  means  of  anticipating 
income  (§12),  and  the  value  of  both  capital  and  interest  is  ex- 
pressed in  money,  it  follows  that  interest  is  the  price  of  the  use 
of  money. 

This  price  for  money  loans  is  termed  the  "rate  of  interest." 
As  money  is  more  desirable  than  other  forms  of  capital  because 
of  its  universal  acceptability  as  a  medium  of  exchange,  and  as  the 
risk  in  money  lending  is  normally  less  (§  36)  than  in  business, 


INTEREST  23 

this  rate  of  interest,  which  represents  the  possible  income  on 
capital  in  the  form  of  money,  becomes  the  standard  by  which 
the  desirability  of  any  other  form  of  investment  is  gauged. 

39.  The   Profits   of   the   Undertaking.  —  Unless   there   is   a 
chance  of  earning  a  larger  rate  of  income  upon  the  capital  re- 
quired in  an  undertaking  than  could  be  earned  by  lending  this 
capital  to  others,  there  would  be  no  incentive  to  assume  the 
risks  of  the  business.     In  order  to  make  a  business  really  profit- 
able, the  net   income  should  exceed  this  "rate  of  interest." 
This  surplus  is  the  goal  of  the  whole  operation  and  is  termed  the 
"profits  of  the  undertaking,"  as  distinct  from  the  term  "profits," 
which  includes  interest  (§  33) .    It  is  the  personal  reward  of  the 
individual  who  has  borne  the  responsibility  of  the  business. 
There  is  no  good  English  word  to  indicate  this  person.     Un- 
fortunately we  have  appropriated  the  word  "undertaker  "  for 
other  uses.     The  French  term  "entrepreneur"  is  commonly 
accepted  by  economists.      The  more  recent  English  substitute 
"enterpriser  "  is  rather  clumsy,  but  will  be  used  in  this  text. 

The  term  "profits  of  the  undertaking  "  would  therefore  ex- 
clude interest  as  a  necessary  "cost"  and  regard  the  margin 
remaining  as  the  real  profit. 

40.  Annual  Profits.  —  On  this  basis,  a  business  paying  annual 
dividends  is  considered  successful  if  the  average  dividends  are 
larger  than  the  rate  of  interest  which  the  firm  has  to  pay  on 
borrowed  capital.     If  the  dividends  are  less  than  this,  the  busi- 
ness is  considered  unprofitable  to  the  owner,  although  it  may  be 
relatively  more  profitable  to  continue  it  than  to  abandon  or  sell 
it,  with  resultant  loss  or  impairment  of  capital.     As  a  matter  of 
fact,  only  the  more  capable  and  experienced  managers  succeed 
in  earning  an  "enterpriser's  profit,"  and  one  per  cent  of  independ- 
ent concerns  annually  become  insolvent,  thus  failing  to  earn  a 
net  income  sufficient  even  to  protect  the  capital  investment.* 

41.  Deferred  Profits.  —  In  an  enterprise  in  which  outlay 
precedes  income  by  an  interval  greater  than  one  year,  the  method 
of  accounting  for  profits  depends  upon  whether  this  condition 

*  The  Percentage  of  Failures,  Dun's  Review,  May  31,  1913.  R.  S.  Dun  &  Co., 
New  York. 


24  FOREST  VALUATION 

of  affairs  is  normal  or  accidental,  expected  or  unforeseen.  If 
profits  should  normally  be  earned  annually,  failure  to  do  so  in 
any  given  year  would  be  regarded  as  a  loss  by  the  proprietor, 
but  this  would  be  mentally  "written  off"  against  the  current 
year  and  not  carried  as  a  debit  to  be  recovered  from  the  income 
of  a  subsequent  year. 

If  the  enterprise  is  planned  to  extend  several  years  before 
realizing  profits,  as  in  the  case  of  the  voyages  of  whaling  ships, 
or  the  production  of  timber  from  plantations,  the  annual  interest 
which  remains  unpaid  is  not  considered  lost,  since  it  is  the  expec- 
tation of  the  owners  that  this  will  be  more  than  made  up  when 
the  "ship  comes  in."  But  the  profits  of  the  undertaking  may 
still  be  computed  separately  from  the  standard  interest  "cost" 
or  income.  This  must  be  done  by  calculating  compound  interest 
on  all  cash  expenses  as  long  as  they  remain  unpaid,  which  gives 
the  sum  that  could  be  earned  by  the  capital  as  loans  in  money 
form  for  an  equal  period. 

The  deferred  income  may  greatly  exceed  the  total  cash  outlay 
and  the  enterprise  yet  fail  to  earn  compound  interest  at  a 
standard  rate.  In  this  case  the  deferred  "profits  of  the  under- 
taking" disappear,  and  the  status  of  the  venture  is  the  same 
as  that  of  the  business  whose  annual  dividends  fall  below  the 
standard  rate  of  interest. 

The  production  of  timber  as  a  business  is  based  largely  on 
the  theory  of  deferred  profits,  and  both  the  determination  of 
these  profits  and  the  methods  of  accounting  employed  should 
be  made  to  conform  to  the  essential  differences  between  such  a 
business  and  one  conducted  on  the  basis  of  annual  profits. 

42.  Income  versus  Profits.  —  In  determining  the  amount  or 
rate  of  profit  which  should  be  earned  in  order  to  properly  com- 
pensate the  enterpriser,  the  status  of  interest  must  be  held 
clearly  in  mind.  It  is  a  "cost"  merely  for  purposes  of  sepa- 
rating that  portion  of  the  income  which  his  capital  could  earn 
from  the  additional  income  earned  by  his  personal  efforts.  In 
impersonal  consideration  of  the  legitimate  profits  of  a  business, 
the  distinction  between  borrowed  capital  and  proprietary  capital 
is  rejected,  and  the  interest  upon  the  entire  capitalization  is 


INTEREST  25 

included  in  the  income  earned  and  not  in  costs.  Should  the 
fallacy  be  introduced  of  considering  interest  as  a  cost  in  comput- 
ing profits,  the  apparent  profit  required  would  be  increased 
abnormally.  For  instance,  it  is  stated  that  a  certain  business 
should  earn  a  profit  of  10  per  cent,  which,  with  interest  at  6  per 
cent,  indicates  an  enterpriser's  profit  of  4  per  cent.  By  consid-  • 
ering  this  interest  as  an  actual  cost,  an  additional  profit  of  10 
per  cent  might  be  expected.  But,  in  reality,  this  10  per  cent 
would  be  the  enterpriser's  profit.  The  total  net  income  must 
then  be  16  per  cent,  and  the  enterpriser's  gain  is  2\  times  as 
great  as  in  the  original  case.  If  an  enterpriser's  profit  of  10 
per  cent  is  necessary,  the  "profits"  of  the  business  must  be  16 
per  cent  and  not  10  per  cent. 

The  larger  the  amount  of  capital  invested  in  a  business,  the 
smaller,  as  a  rule,  will  be  this  margin  between  income  and 
interest,  which  represents  the  enterpriser's  gain.  Both  income 
and  "gain,"  while  larger  in  amount,  average  less  in  proportion 
than  on  small  investments.  This  shrinkage  does  not  come 
entirely  on  the  margin  of  gain,  since  funds  can  probably  be 
borrowed  at  lower  rates  in  such  undertakings.  The  longer  the 
time  elapsing  before  income  is  received,  the  less  will  be  this 
margin  of  profit  over  compound  interest  at  standard  rates. 
For  very  long  investments,  the  enterpriser's  gain  tends  to  dis- 
appear, and  is  entirely  dependent  on  the  rate  of  interest  chosen 
as  representing  the  legitimate  income  on  the  capital  itself. 

In  both  the  above  cases,  in  spite  of  the  shrinking  of  enter- 
priser's profits,  the  income  or  profit  over  expenses  remains  in 
the  form  of  interest  returns,  and,  especially  on  long  time  in- 
vestments, the  final  results  may  still  be  considered  by  the  inves- 
tor as  highly  satisfactory. 

This  attitude  is  partly  due  to  ignorance.  The  owner  of  un- 
productive property,  such  as  unimproved  real  estate,  seldom 
keeps  a  cost  account  which  shows  him  the  total  outlay  repre- 
sented by  the  purchase  price  plus  taxes  and  improvements,  and 
still  more  rarely  does  he  add  the  "cost"  of  the  unearned  interest 
on  this  total  from  year  to  year.  When  he  sells  this  property 
after  the  lapse  of  several  years,  for  more  than  double  what  he 


26  FOREST  VALUATION 

paid  for  it,  he  does  not  realize  that  a  savings  bank  at  4  per  cent 
might  have  paid  him  more  for  the  uninterrupted  use  of  the  same 
capital  than  his  profit  amounts  to. 

Yet  this  attitude  of  investors  towards  deferred  profits  is  not 
explained  wholly  by  ignorance.  If  an  investor  is  in  a  position  to 
get  along  without  income  for  a  long  period,  at  the  end  of  that 
time  the  "loss"  of  annual  income  has  but  little  significance 
and  he  sees  only  the  accumulated  total  of  his  profit.  He  com- 
pares this  with  his  original  outlay  and  judges  results  on  that 
basis.  This  tends  to  make  him  satisfied  with  a  return  which  in 
reality  represents  low  rates  of  interest  on  such  investments. 

43.  Influences  Determining  the  "Rate  of  Interest."  —  The 
current  rate  of  interest  is  a  price,  determined  by  the  demand 
and  supply  of  money  for  borrowing  purposes.     This  price  or 
rate  has  no  greater  stability  than  the  average  prices  of  other 
commodities.     It  fluctuates  during  the  year,  and  over  longer 
periods,  in  response  to  changing  economic  conditions.     Nor  is 
this  rate  the  same  for  all  classes  of  loans.     It  varies  with  the 
security  offered,  the  length  of  the  period  covered  by  the  loan, 
and  the  personality  of  the  individuals  negotiating  it.     In  spite 
of  these  variations,  an  average  rate  of  interest  may  be  roughly 
approximated  for  a  given  time  and  place;  but  this  is  determined 
far  more  closely  if  the  circumstances  affecting  the  particular 
loan  are  also  known. 

44.  The  Influence  of  Personality  on  the  Rate  of  Interest.  — 
Just  as  prices  are  the  resultant  of  human  opinions  interpreting 
desires  or  demand  and  weighing  them  against  efforts  or  supply, 
so  the  rate  of  interest  depends  even  more  completely  upon  the 
human  character  and  mind. 

Impatience  for  income,  and  preference  for  present  over  future 
income,  tends  to  raise  the  price  the  individual  will  pay  for  this 
privilege.  Persons  who  lack  foresight,  are  improvident  and 
are  lacking  in  self-control  will  borrow  at  high  rates.  The  same 
is  true  of  persons  who  lack  capital  and  are  in  need  of  present 
income.  On  the  other  hand,  individuals  who  desire  to  provide 
for  the  future,  who  possess  the  power  of  self-denial  and  who  are 
already  possessed  of  considerable  capital  will  borrow,  if  at  all, 


INTEREST  27 

only  at  reasonable  rates.  As  investors,  the  former  group  desire 
to  "get  rich  quick"  and  by  seeking  abnormal  profits  usually 
lose  what  capital  they  may  possess.  The  latter  group  are  apt 
to  favor  long  time  investments  which  give  a  certain  return  even 
at  a  low  rate. 

45.  Risk  and  Expense.  —  As  most  loans  of  money  are  made 
on  the  basis  of  a  security  pledged  as  a  guarantee  for  repayment, 
and  worth  more  than  the  amount  of  the  loan,  the  risk  of  loss 
of  principal  or  interest  is  correspondingly  reduced.     In  case  of 
unreliable  parties,  notes  are  guaranteed  by  some  one  who  is 
able  to  pay.     Risky  loans  are  made  at  higher  rates  than  safe 
loans,  the  extra  rate  being  intended  to  cover  average  losses. 
The  exorbitant  rates  charged  by  loan  sharks  are  not  justified  on 
this  basis,  although  loans  of  this  character  require  a  somewhat 
higher  rate  than  business  loans.     Such  rates  are  due  to  personal 
elements,  exaggerated  by  defective  laws  and  bad  economic  con- 
ditions, which  permit  the  exploitation  of  a  class  of  persons  unable 
to  protect  themselves. 

Expense  of  placing  loans  and  of  collecting  interest  tend  to 
increase  the  rate  of  interest  charged.  This  expense  is  greater  for 
short  loans,  and  the  funds  are  apt  to  be  idle  part  of  the  time. 

It  follows  that  the  lowest  rates  of  interest  are  received  on 
absolutely  safe  securities,  which  run  for  a  long  period  and  upon 
which  the  interest  payments  are  made  without  expense  to  the 
owner.  Government  securities  and  bonds  of  high  grade  fulfil 
these  conditions. 

46.  Fluctuating  Value  of  Money.  —  Should  money  fall  in 
value  or  in  purchasing  power,  the  rate  of  interest  tends  to  rise 
to  a  degree  corresponding  to  the  average  annual  loss  in  the  value 
of  the  capital.     Only  by  this  means  can  a  lender  of  capital  escape 
actual  loss.     If  the  fall  in  value  amounts  to  i  per  cent  per  year, 
securities  upon  which  the  normal  rate  of  interest  is  4  per  cent 
will  be  worth  in  purchasing  power  only  99  per  cent  of  their 
original  value  at  the  close  of  the  year.    A  rate  of  5  per  cent 
enables  the  investor  to  replace  this  difference  by  adding  it  to  the 
capital. 

Such  losses  usually  escape  the  notice  of  the  owner,  who  imag- 


2g  FOREST  VALUATION 

ines  himself  as  wealthy  as  before  even  if  he  spends  the  entire 
income  from  his  investment. 

47.  The  Rate  of  Interest  for  Business  Investments.  —  The 
rate  of  interest  for  a  business  is  the  rate  at  which  money  will 
seek  investment  in  the  enterprise.     It  is  a  question  whether 
or  not  this  basic  rate  should  include  an  enterpriser's  profit. 
The  rate  which  the  lender  of  capital  will  accept  on  the  security 
of  the  business,  or  what  the  proprietor  can  obtain  as  the  basis 
for  a  loan,  is  a  conception  tallying  rather  more  closely  with  actual 
conditions.     Such  a  rate  may  be  said  to  attract  capital,  but  it 
may  not  attract  the  enterpriser,  who  hopes  to  do  better.     The 
"rate"  adopted  as  the  standard  for  an  investment  becomes 
the  basis  for  computing  both  the  cost  of  production  (§  25)  and 
the  value  of  the  assets  (Chapter  IV) . 

48.  The  Effect  of  Deferred  Income  upon  the  Rate  of  Interest. 
—  A  mathematical  comparison  of  simple  and  compound  interest 
leads  to  the  conclusion  that,  since  the  latter,  as  applied  to  de- 
ferred returns,  is  the  exact  equivalent  of  the  former  when  returns 
are  annual,  a  given  basic  rate  should  be  the  same  whether  the 
investment  pays  annual  or  deferred  income. 

But  under  the  definition  that  the  "rate  of  interest"  means 
the  rate  which  will  attract  money  to  a  business,  the  above 
conclusion  must  be  tested  by  the  "price  making"  factors 
which  influence  the  minds  of  investors.  Should  these  factors 
be  found  to  differ  for  investments  of  the  two  classes,  the  basic 
rate  of  interest  applicable  to  each  case  will  differ  to  a  corre- 
sponding degree. 

49.  Comparison  of  Results  of  Simple  and  Compound  Interest. 
-  The  economic  results  obtained  in  actual  practice  from  an 

undertaking  which  produces  simple  or  annual  interest  are  not 
the  same  as  those  obtained  by  compound  interest,  however 
similar  may  be  their  mathematical  relation. 

To  make  the  returns  from  a  business  which  starts  with  a 
definite  amount  of  capital,  and  earns  annual  net  profits  at  x 
per  cent,  equal  to  those  from  the  investment  of  a  similar  sum 
which  will  produce  compound  interest  after  a  term  of  years  at 
the  same  rate,  x  per  cent,  requires  several  assumptions.  The 


INTEREST  29 

entire  earnings  of  the  business  would  have  to  be  retained  as 
capita]  and  not  a  cent  withdrawn  as  dividends.  This  capital 
must  then  be  utilized  in  such  a  manner  that  it  will  produce  net 
earnings  equal  in  rate  to  the  earnings  on  the  original  capital. 
Each  year  this  process  must  be  repeated,  resulting  in  an  expan- 
sion of  the  business  at  a  geometric  rate.  If  this  result  is  ob- 
tained, the  total  capital  at  the  end  of  the  period  will  not  be 
worth  one  cent  more  than  the  funds  accumulated  in  the  second 
investment,  where  ah1  income  is  deferred  until  the  end  of  the 
period. 

Should  the  proprietor  withdraw  any  portion  of  the  earnings 
during  the  entire  period,  or  should  the  business  fail  to  expand 
annually  at  the  required  per  cent,  the  resultant  rate  of  com- 
pound interest  earned  by  annual  profits  will  be  lowered  below 
that  demanded  in  the  comparison. 

50.  Limitation  of  Opportunity.  —  Such  compound  expansion 
of  a  business  is  possible  only  where  the  economic  opportunity 
(§  27)  is  practicaUy  unlimited,  or  increases  at  a  rate  which  keeps 
pace  with  the  growth  of  the  business.  This  occurs  only  as  a 
temporary  condition,  both  in  business  and  in  ah1  other  forms  of 
activity. 

Animal  and  plant  life  have  the  capacity  for  expansion  at  geo- 
metric ratios  comparable  to  enormous  rates  of  compound  in- 
terest; such  events  seldom  occur,  but  when  they  do,  the  result 
is  calamitous.  English  sparrows  imported  into  America  found 
an  environment  not  used  by  any  existing  species  of  bird.  Until 
this  niche  had  been  completely  occupied,  the  sparrow  increased 
at  a  compound  rate.  The  species  is  now  merely  holding  its  own. 

In  manufacturing,  the  production  of  new  articles  and  the 
growth  of  a  demand  for  them,  as  in  the  case  of  automobiles, 
creates  an  opportunity  which  permits  of  a  trade  expansion  at 
geometric  or  compound  rates  for  a  while.  This  expansion  took 
place  when  bicycles  were  first  made  popular.  It  cannot  con- 
tinue in'any  line  at  the  same  rate  over  an  extended  period.  A 
lessening,  not  of  the  annual  demand,  but  merely  of  its  rate 
of  increase,  has  the  effect  of  preventing  further  expansion  at  a 
like  rate,  and  with  the  establishment  of  equilibrium,  not  only 


3o  FOREST  VALUATION 

will  compound  interest  fall  to  a  lower  rate,  but  annual  profits 
will  be  reduced  as  well.  This  explains  the  fact,  accepted  by 
economists,  that  the  larger  the  aggregation  of  capital  employed 
in  an  undertaking,  the  smaller  will  be  the  annual  rate  of  profits 
which  justifies  the  investment. 

The  conclusion  is  irresistible,  that  the  mathematical  equality 
between  simple  and  compound  returns  does  not  hold  good. 
The  latter  tends  to  fall  below  the  former,  and,  what  is  more 
important,  this  discrepancy  is  accepted  as  equitable  by  investors. 
The  recognition  of  this  fact  will  go  far  towards  clearing  up 
the  false  impressions  which  at  present  obscure  the  question  of 
rates  of  interest  applicable  to  forest  investments. 

51.  Effect  of  the  Rate  of  Interest  upon  Accumulations  of 
Compound  Interest.  —  The  cumulative  effect  of  compound 
interest  bears  an  intimate  relation  to  the  rate  of  interest.  Low 
rates  cause  a  very  slow  increase  and  may  be  applied  with  some 
reason  to  investments  which  run  for  a  very  long  period.  High 
rates  cause  a  very  rapid  increase  which  soon  passes  the  bounds  of 
possible  attainment  in  practice.  The  following  diagram  reveals 
this  relation.  (See  Diagram  I.) 


TABLE   I 
COMPARISON  OF  THE  RESULTS  OF  SIMPLE  AND  COMPOUND  INTEREST 

ON  $100  AT  THE   END  OF  A    PERIOD   OF   50   YEARS 


Rate  of 

Value  of  capital 

Rate  of  simple  in- 
terest to  be  earned 

interest 

and  interest  at 

and  saved  to 

earned 

end  of  period 

give  equal  final 

results 

Per  Cent 

Per  Cent 

I 

$164 

1.28 

2 

269 

3.38 

3 

438 

6.76 

4 

710 

12.20 

5 

1,146 

20.92 

6 

1,842 

34.84 

7 

2,946 

56.92 

8 

4,690 

91.80 

10 

n.739 

232.78 

A  comparison  of  the  economic  results  of  simple  and  compound 
interest  is  further  brought  out  by  the  above  table  which  gives 


INTEREST 


DIAGRAM  I 

PERIODS  REQUIRED  FOR  $1.00  TO  MULTIPLY,  AT  DIFFERENT  RATES  OF 
COMPOUND  INTEREST* 


104      84  7* 


8lt 


70       75 


*  A  rate  of  10  per  cent,  compounded,  multiplies  20  times  in  31  years.  A  rate  of 
i  per  cent  compounded,  doubles  in  70  years.  Even  6  per  cent  would,  in  70  years, 
multiply  the  principal  59  times. 


3  2  -  FOREST  VALUATION 

the  total  amount  to  which  the  sum  of  $100  will  increase  in  50 
years,  provided  the  investor  complies  with  the  conditions  out- 
lined in  Article  49. 

The  final  column  shows  the  rate  which  the  original  invest- 
ment would  have  to  earn  annually  to  get  the  same  results,  pro- 
vided the  entire  income  were  placed  in  a  deposit  vault  and 
saved  until  the  end  of  the  period  without  reinvestment.  Should 
the  proprietor  spend  the  annual  income,  he  would  have  merely 
the  original  capital  of  $100  left  at  50  years. 

52.  The  Rate  of  Interest  in  Forest  Investments.  —  To  de- 
termine the  basic  rate  of  interest  applicable  to  investments 
in  forestry,  two  factors  must  be  analysed,  namely,  the  relative 
security  of  the  investment,  and  the  financial  nature  of  the  enter- 
prise. It  is  claimed  by  advocates  of  a  high  rate  on  forest  invest- 
ments that  this  is  justified  by  the  ever-present  risks  from  fire  and 
other  destructive  agencies,  and  also  by  the  length  of  the  period 
elapsing  between  outlay  and  income,  which  makes  the  invest- 
ment less  desirable  unless  it  can  be  shown  to  be  more  profitable. 

The  first  of  these  claims  must  be  admitted.  Risk  should  be 
provided  against  by  demanding  higher  interest.  This  subject 
is  discussed  in  Chapter  XIII.  Risks  must  be  judged  on  the 
basis  of  comparison  with  those  assumed  in  other  lines  of  in- 
vestment, and  due  weight  must  be  given  to  the  present 
development  of  measures  of  protection  on  the  part  of  states 
and  associations. 

The  second  claim  is  fallacious.  To  demand  a  higher  rate  of 
interest  the  longer  the  returns  are  deferred  is  a  subversion  of  the 
economic  laws  applicable  to  all  forms  of  investment.  The  desir- 
ability of  the  investment  as  affected  by  the  difference  between 
annual  and  deferred  returns  will  not  modify  the  rate  of  interest 
which  should  apply,  but  rather,  will  determine  the  class  of 
persons  who  are  apt  to  choose  such  an  investment.  And  since 
those  persons  who  are  the  most  apt  to  favor  long-term  invest- 
ments with  deferred  income  are  those  possessed  of  foresight, 
making  provision  for  their  children,  and  with  sufficient  capital 
for  their  personal  needs  (§44),  such  persons  will  accept  a  lower 
rather  than  a  higher  rate  of  interest,  and  in  many  cases  will  not 


INTEREST  33 

even  compute  the  probable  rate,  being  content  with  the  general 
prospect  of  a  future  value  greatly  in  excess  of  present  investment. 

53.  Comparison  of  Interest  Rates  in  Forestry  with  Other 
Investments.  —  Proper  rates  for  forest  investments  can  only  be 
judged  on  the  basis  of  comparison  with  other  forms  of  enterprise. 
If  the  scope  of  the  comparison  is  confined  to  forest  production 
and  the  account  covers  the  period  requisite  for  growth,  a  com- 
parison between  forestry  and  business  producing  annual  income 
is  impossible.  The  goal  of  forest  management  is  the  forest 
which  will  yield  annual  returns,  but  each  crop  represents  the 
accumulated  outlay  throughout  its  life  and  must  be  so  judged 
in  comparing  interest  rates. 

The  only  enterprises  familiar  to  the  public,  which  are  reckoned 
on  a  basis  of  compound  interest,  are  savings  banks  and  life 
insurance  companies.  The  former  have  paid  an  average  of 
3  per  cent,  but  of  late  years  4  per  cent  is  common.  Most  banks 
do  not  permit  the  accumulation  of  compound  interest  on  accounts 
to  run  more  than  20  years  without  some  sign  of  active  interest 
on  the  part  of  the  owner,  manifested  either  by  withdrawals  or 
additional  deposits.  If  the  owner  is  alive  and  can  refrain  from 
depleting  his  account  for  fifty  years  and  the  bank  remains 
solvent,  he  can  obtain  compound  interest  for  that  period.  Such 
cases  practically  never  occur. 

The  average  period  covered  by  the  risk  of  a  life  insurance  policy 
is  not  over  13!  years,*  and  most  companies  calculate  that  they 
can  earn  compound  interest  at  about  4  per  cent  on  the  money 
invested  in  policies  for  this  average  period. 

For  periods  longer  than  fifty  years  there  is  no  basis  for  com- 
parison by  which  the  rates  reasonably  applicable  to  forest 
investments  can  be  judged.  Based  upon  the  economic  laws 
outlined  in  Articles  47  to  50,  it  must  follow  that  those  rates 
will  be  less  than  4  per  cent  provided  the  investment  offers  equal 
security  with  life  insurance  and  savings  banks.  Should  the 
security  be  considered  less  safe,  the  increased  rate  demanded 
would  offset  the  reduction  in  rate  called  for  by  the  length  of 
the  period  of  investment,  and  the  investment  should  not  require 

*  The  Brown  Book  of  Life  Insurance  Economics.    Edition  of  1911-12,  p.  13. 


34 


FOREST  VALUATION 


a  rate  appreciably  higher  than  4  per  cent  for  periods  of  over 
50  years. 

If  these  arguments  are  admitted,  it  is  possible  to  show  that 
the  income  which  may  actually  be  earned  by  forest  investments 
covering  long  periods  will  be  equivalent  to  the  rates  demanded 
by  the  character  of  the  investment,  even  though  the  earnings 
may  fall  as  low  as  3  per  cent  for  periods  of  over  50  years,  and 
i\  per  cent  to  2  per  cent  for  periods  exceeding  100  years. 


CHAPTER   IV 
VALUATION   OF   ASSETS 

54.  Valuation  Accounts.  —  A  valuation  account  is  a  specific 
statement  (§  19)  of  the  value  of  assets,  whether  material  or  con- 
sisting of  intangible  rights.     It  informs  the  owner  of  the  present 
condition  of  the  property,  and  enables  him  to  compare  this  con- 
dition and  value  with  the  total  net  cost  or  investment  (§22),  and 
thus  determine  whether  the  business  as  a  whole  is  gaining  or 
losing  (§  28).     To  accomplish  this  purpose,  the  account  should 
show  what  the  business  or  property  is  actually  worth  at  the 
present  moment,  not  merely  what  it  was  worth  when  the  assets 
were  first  acquired. 

55.  The  Inventory.  —  In  order  to  determine  value  we  must 
know  the  quantity  of  goods  on  hand  and  what  each  unit  is  worth. 
This  process  of  taking  stock  is  termed  an  inventory.    It  is  not 
complete  with  the  mere  listing  of  goods,  but  includes  their  valu- 
ation.    In  forest  management  the  process  of  estimating  standing 
timber  and  other  forest  resources,  often  termed  reconnaisance, 
is  the  means  of  obtaining  this  data. 

56.  Cost  as  a  Basis  of  Value.  —  Conservative  accounting 
seeks  to  avoid  inflation  of  the  value  of  assets,  with  its  corre- 
sponding indication  of  false  profits  in  the  balance  sheet.     If  an 
asset  has  been  purchased  in  good  faith,  the  purchase  price  is 
taken  to  represent  its  true  value.    All   items  of  investment 
representing  assets  of  such  a  character  that  they  would  be 
included  in  the  capital  account  will  be  accepted  at  cost,  less 
depreciation,  in  the  valuation  of  assets.    This  does  not  mean 
that  the  cost  of  an  article  represents  its  present  value,  but  merely 
that  cost  is  definitely  known  and,  when  corrected  for  deprecia- 
tion, is  accepted  as  a  conservative  basis  for  value. 

57.  Expenses  and  Interest  versus  Value.  —  While  account- 
ants approve  of  the  acceptance  of  capital  expenditures  or  original 

35 


36  FOREST  VALUATION 

cost  of  purchase  of  tangible  assets  as  a  basis  of  value,  they 
condemn  the  assumption  that  subsequent  expenses,  or  items 
customarily  entered  under  outlay  and  income,  or  profit  and  loss, 
add  anything  to  the  value  of  assets  or  furnish  a  basis  for  valuing 
these  assets.  The  theory  is  that  such  expenditures  are  made 
for  the  direct  purpose  of  producing  income  sufficient  to  offset 
them,  and  that  if  this  result  is  not  secured,  the  loss  must  be  shown 
as  a  deficit,  and  not  concealed  by  adding  an  equivalent  of  this 
loss  to  the  value  of  the  assets. 

This  theory  is  justified  for  business  undertakings  supposed  to 
produce  annual  income,  for  if  the  income  which  should  cancel 
expenses  fails  to  do  so,  the  deficit  cannot  be  construed  to 
represent  anything  but  absolute  loss,  leading  to  insolvency. 

This  reasoning  is  then  extended  to  apply  to  undertakings 
in  their  formative  period  (§  23),  and  the  practice  of  retaining 
investments  in  the  inventory  at  their  original  cost  is  highly 
commended,  in  spite  of  the  fact  that  practically  all  expenses 
during  this  period  require  additions  to  capital  (§  24),  and  this 
treatment  of  assets  is  thus  bound  to  result  in  an  apparent  deficit 
or  state  of  insolvency. 

Yet  no  one  would  undertake  such  long  time  investments 
unless  he  expects  an  increase  in  the  value  of  his  assets  in  a  meas- 
ure corresponding  to  or  paralleling  the  accumulation  of  cost 
and  interest.  That  this  fact  is  assumed  has  a  remarkable  con- 
firmation in  the  revolutionary  practice  of  accounting  authorized 
in  case  of  railroad  properties  during  the  course  of  construction 
and  before  it  is  possible  to  earn  an  income.  In  Germany  and 
England  it  is  permitted  by  law  to  include  as  an  addition  to  the 
value  of  the  assets,  not  only  the  revenue  expenditures  during 
construction,  but  the  interest  on  bonds  and  dividends  to  stock- 
holders.* This  is  the  very  process  so  vigorously  and  justly 
condemned  in  case  of  business  undertakings  which  should  pay 
annual  dividends,  nor  would  it  be  tolerated  in  the  case  of  rail- 
roads except  during  the  period  of  construction. 

A  case  closely  parallel  to  the  above  is  found  in  forest  planta- 

*  "Modern  Accounting,"  by  Henry  Rand  Hatfield,  pp.  76,  77.  D.  Appleton 
&  Co..  IQOQ. 


VALUATION  OF  ASSETS  37 

tions.  Shall  the  value  of  such  property  be  based  on  the 
purchase  price,  plus  expenses,  plus  unpaid  or  deferred  interest, 
representing  the  total  "cost"  or  "cost  value"  of  the  property? 
As  in  the  case  of  the  railroad  this  might  be  justified.  But  such 
"cost"  is  only  an  indication  of  value  in  either  of  these  instances. 
Unless  the  property  is  of  such  a  character  and  its  promise  of 
future  income  is  such  that  this  increase  in  value  is  sure  to  occur 
and  is  evidently  taking  place,  no  one  would  be  deceived  into 
thinking  that  such  a  cost  calculation  corresponded  in  the  least 
with  value.  Even  then  the  value  might  be  more,  or  less,  and 
there  is  no  reason  for  assuming  that  it  is  accurately  gauged  by 
cost. 

58.  Essential  Difference  between  Cost  and  Value.  —  The 
reader  must  keep  clearly  in  mind  that  the  valuation  of  assets  is 
a  process  essentially  different  from  the  account  of  cost  and  ex- 
penses (Chapter  I,  Articles  2  to  n  inclusive).     If  costs  are  taken 
as  the  basis  of  value,  as  is  done  in  some  instances  (§56),  they 
are  merely  the  source  of  the  information  used,  but  this  informa- 
tion might  as  readily  be  obtained  from  entirely  different  sources, 
and  frequently  must  be  so  acquired.     Value  is  determined  for 
the  purpose  of  comparison  with  costs  to  indicate  profit  or  loss. 
If  it  were  identical  with  cost,  no  comparison  would  be  possible 
and  the  owner  could  not  determine  his  probable  profits. 

59.  Sale  Value  as  a  Basis  of  Value.  —  In  case  a  business 
changes  hands  by  sale,  the  sale  value  so  determined  is  accepted 
as  the  value  of  the  business.     In  this  transaction  the  price  paid 
for  the  assets  must  be  entered  as  their  value  on  the  books. 
Such  sales  thus  establish  a  new  recorded  or  book  value  for  these 
assets.     The  fact  of  the  sale  is  the  most  convincing  evidence  of 
value,  although  even  this  is  not  final  proof,  for  one  or  the  other 
of  the  parties  may  have  been  deceived  or  handicapped  in  the 
transaction.     Nor  will  a  past  sale  be  accepted  as  absolutely 
determining   a  future   sale  value   even  for  the   same  property; 
in  fact  it  is  usually  the  reason  for  desiring  a  different  value. 
Sales  of  property  or  business  have  a  profound  effect  upon  pro- 
prietary accounts,  in  that  the  former  owner  receives  at  once  all 
his  income  and  capital  and  can  balance  his  books  and  determine 


38  FOREST  VALUATION 

his  total  net  profit,  while  the  purchaser  is  saddled  with  a  cost  or 
investment  which  forms  the  opening  entry  in  a  similar  account, 
and  no  future  acts  will  serve  to  reduce  this  initial  cost. 

60.  Appraisal  of  Value  (§  18).  —  In  determining  the  true  value 
of  assets,  either  as  a  guide  to  the  owners  in  negotiating  a  sale, 
or   for   compensation   for   damages   or   in  condemnation   pro- 
ceedings, the  appraiser  bases  his  opinion  upon  the  most  reliable 
sources  of  information  at  hand.     If  a  basis  for  sales  is  sought, 
the  average  sale  value  of  similar  property  in  the  immediate 
past  is  given  most  weight.     But  where   the  owner  does  not 
desire  to  sell,  the  appraiser  must  seek  to  establish  the  value 
to  the  owner  if  the  property  remains  in  his  possession,  and  this 
rests  wholly  on  its  usefulness  to  him,  not  on  what  someone  else 
would  pay  for  it. 

61.  Future  Income  as  the  Basis  of  Value.  —  The  only  true 
basis  of  value  recognized  by  economists  is  income  (§§4,   26). 
When  a  sale  of  property  occurs,  the  "income"  from  the  sale 
should  coincide  with  the  value  of  the  property.     The  value 
which  the  owner  or  purchaser  places  on  the  property  is  deter- 
mined by  the  value  of  all  the  future  income  which  he  expects  to 
derive  from  it. 

In  explaining  values  on  this  basis  the  true  nature  of  income 
must  be  kept  in  mind.  " Final"  income  takes  the  form  of 
actual  enjoyment  of  the  uses  or  services  of  possessions.  Real 
estate  is  valuable  to  an  owner,  not  merely  for  its  money  income, 
but  for  the  personal  enjoyment  which  he  gets  from  the  rights 
of  possession.  In  this  must  be  included  the  associations  and 
neighborhood  of  which  it  makes  him  a  part.  The  sentiment 
attached  to  the  retention  of  an  inherited  homestead,  the  prej- 
udice against  leaving  surroundings  grown  familiar  by  long  resi- 
dence will,  by  contributing  to  the  peace  of  mind  of  the  owner, 
enhance  the  value  of  his  land  in  his  opinion  in  a  manner  fully 
as  concrete  as  money  income.  Only  poverty  or  actual  want 
will  counterbalance  these  very  real  values.  This  element  of 
social  income  must  never  be  lost  sight  of  in  the  valuation  of 
property.  But  the  appraisal  of  income  must  ordinarily  be  based 
upon  money  returns  which  can  reasonably  be  expected  in  the 


VALUATION  OF  ASSETS  39 

future,  and  the  present  value  of  the  property  rests  upon  the 
mathematical  relation  between  the  future  income  and  its  dis- 
counted value. 

62.  Capital  Value  or  Expectation  Value.  —  Capital  value,  or 
expectation  value,  is  the  net  value  of  property  based  upon  future 
income.  It  is  the  capitalized  value  of  future  income  minus 
future  expenses.  The  terms  "capitalized"  and  "discounted" 
are  synonymous.  Therefore  capital  value  is  the  discounted  net 
value  of  future  income.  Finally,  since  all  future  income  is 
included  in  present  value,  capital  value  is  the  sum  of  the  dis- 
counted values  of  all  items  of  future  net  income.  This  definition 
holds  good  whether  the  income  is  received  at  regular  daily, 
monthly  or  annual  intervals,  or  at  intervals  of  two  or  more, 
even  of  100  years,  or  is  irregular  in  amount  and  paid  at  irregular 
intervals. 

An  example  of  regular  annual  income  is  the  interest  on  a 
money  loan.  This  interest,  capitalized,  corresponds  to  the  value 
of  the  loan  of  capital.  This  relation  established  between  capi- 
tal and  income  through  the  rate  of  interest  (§  38)  is  the  means 
of  determining  the  capital  value  of  all  other  forms  of  property. 

For  money  alone  the  value  of  the  capital  and  of  its  use  deter- 
mines the  value  of  the  income  or  rate  of  interest,  and  the  value 
of  money  is  neither  raised  nor  lowered  by  fluctuations  in  the 
rate  of  interest. 

For  other  property  the  relation  is : 

1.  Capital  or  property  earns  income. 

2.  The  value  of  this  income  is  appraised. 

3.  This  value  is  then  discounted  to  obtain  the  value  of  the 
capital. 

4.  The  "rate  of  interest"  is  the  measure  of  discount. 

The  term  "capital  value"  has  so  far  found  no  place  in  the 
literature  of  forest  valuation.  Instead,  such  authorities  as 
Schlich  have-  translated  continental  terms  into  the  English 
"expectation  value."  This  term  is  descriptive  of  the  fact 
that  such  values  are  based  on  future  expectations,  not  fully 
determined;  but  it  is  open  to  objections,  since  it  conveys  the 


4o 


FOREST  VALUATION 


impression  that  such  values  are  different  or  obtained  in  a  different 
manner  from  the  capitalized  values  computed  for  all  other  forms 
of  property.  On  the  contrary,  the  process  is  identical  and  it 
would  be  a  distinct  advantage  to  recognize  this  fact  in  terminol- 
ogy. A  third  term,  also  identical  in  meaning  with  the  two  above 
mentioned,  is  "capitalized  rental  value,"  sometimes  abbreviated 
to  "rental  value."  Two  objections  to  the  term  "rental  value" 
are  that  it  may  be  confused  with  rent,  which  is  only  one  form 
of  income,  and  that  it  may  be  taken  to  mean  the  value  of  one  of 
the  current  or  periodical  payments  of  income  instead  of  its 
true  meaning,  which  is  the  sum  of  the  discounted  values  of  all 
items  of  future  income.  The  term  "capitalized  rental  value" 
seeks  to  emphasize  this  latter  meaning,  but  the  use  of  the  word 
"rental"  might  be  taken  to  mean  that  such  values  are  deter- 
mined only  for  property  producing  income  at  regular  intervals. 
Since  it  makes  no  difference  what  the  character  or  interval  of 
payment  is,  the  term  "capital  value"  is  the  most  comprehen- 
sive. The  one  great  objection  to  this  term  is  that  the  word  capi- 
tal is  commonly  used  to  denote  the  amount  of  an  investment, 
or  the  total  funds  furnished  by  capitalists  (§§  12-13),  and  is  in  this 
sense  allied  with  cost  rather  than  value  of  assets  (§73).  Were  all 
assets  in  the  form  of  money,  this  would  make  no  difference  (§62), 
but  as  cost  and  value  for  other  assets  diverge  widely,  some 
term  should  be  used  which  is  clearly  understood  as  referring  to 
value  rather  than  cost.  Another  possibility  is  the  term  "income 
value,"  or  "capitalized  income  value."  "Income  value"  is 
open  to  the  same  objection  urged  against  "rental  value,"  —  that 
it  might  be  understood  to  mean  the  value  of  one  year's  income, 
or  of  one  payment.  "Capitalized  income  value"  comes  nearest 
to  fully  describing  the  value  indicated  and  the  means  of  ob- 
taining it. 

The  valuation  of  forest  property  differs  from  that  of  property 
earning  annual  income  only  from  the  fact  that  the  income  may 
occur  at  intervals  separated  by  long  periods.  Hence  the  tend- 
ency, expressed  by  the  term  "expectation  value,"  to  emphasize 
this  "expectation."  As  will  be  shown  in  Chapter  V,  the  formulae 
employed  in  the  capitalization  of  annual  and  of  intermittent 


VALUATION  OF  ASSETS  41 

income,  such  as  is  received  from  forest  crops,  are  identical  in 
character,  and  it  is  more  important  to  recognize  this  essential 
similarity  than  to  seek  to  differentiate  forest  valuation  from  other 
forms  of  appraisal.  In  the  text,  the  synonymous  terms  "capital 
value"  and  "expectation  value"  will  be  used  interchangeably, 
rather  than  the  more  cumbrous  term  "capitalized  income 
value." 

63.  Future    Prices    and    Values.  —  The    determination    of 
capital  value  rests  upon  the  ability  of  the  appraiser:  first,  to 
ascertain  the  amount  and  character  of  the  income,  its  duration 
and  the  total  for  the  entire  life  of  the  enterprise;  and  second, 
to  appraise  the  probable  value  of  this  income  for  the  time  when 
it  is  received,  by  a  conjecture  as  to  prices  for  the  future  products 
(Chapter  XII).     But  the  future  is  shrouded  in  uncertainty, 
which  becomes  more  impenetrable  the  longer  the  period  over 
which   such   predictions   must  extend.     The  past  is  an  open 
book.    The  knowledge  thus  obtained  by  experience  is  the  guide 
in  the  process  of  appraisal.     It  is  comparatively  ea^sy  to  deter- 
mine the  probable  productiveness  of  property  for  any  business 
which  presents  the  results  of  past  experience.      In  new  and 
untried  ventures  this  is  uncertain.     But  future  prices  are  far 
more  of  a  problem,  since  they  are  the  resultant  of  the  complex 
of  all  the  economic  forces  of  society.    Attempts  may  be  made  to 
predict  changes  in  prices,  due  either  to  changing  price  levels 
based  on  fluctuation  of  the  value  of  money,  or  changes  in  the 
supply  and  demand  for  the  specific  product.     Such  predictions 
can  only  be  based  on  present  tendencies  interpreted  in  the  light 
of  past,  especially  recent,  experience. 

When  reliable  authority  is  lacking  for  prophesying  the  prob- 
able nature  and  amount  of  changes  in  prices,  although  they  are 
certain  to  occur,  the  appraiser  is  forced  to  accept  present  prices 
as  the  basis  for  future  income.  This  principle  finds  its  expres- 
sion in  appraisals  for  damages,  when  speculative  increase  in 
future  income  is  not  admitted  in  valuations. 

64.  Future  Expenses.  —  The  net  present  value  of  income  is 
equal  to  the  margin  over  future  expenses  (§  10).     These  future 
probable  expenses  must  be  appraised  as  carefully  as  income. 


42  FOREST  VALUATION 

Most  elements  of  expense  can  be  judged  by  past  costs  for  similar 
undertakings.  Future  expenses  may  and  will  vary  from  pres- 
ent standards,  for  part  of  this  expense  is  determined  by  prices, 
part  by  wages  and  part  by  legislation  and  taxation.  Uncer- 
tainties regarding  the  trend  of  any  of  these  elements  of  cost 
interfere  with  the  accuracy  of  the  appraisal  of  value.  A  fruit- 
ful source  of  uncertainty  is  future  taxation.  Legislation  tending 
to  substitute  a  definite  arrangement  for  this  fluctuating  item 
is  a  great  aid  in  appraising  the  value  of  forest  property. 

65.  The  Time  Element  in  Capital  Value.  —  When  once  the 
future  income  and  future  expenses  have  been  appraised,  the 
determination  of  the  capital  value  of  the  property  is  a  mathe- 
matical calculation,  dependent  on  the  rate  of  interest  chosen  as 
the  basis  of  comparison  between  the  present  and  the  future 
values  involved.     Each  item  of  income  is  discounted  for  the 
period  of  time  intervening  between  the  present  moment  and 
the  receipt  of  the  income  payment  (§  n).     The  sum  of  these 
values  equals  the  amount  of  money  which  is  equivalent  in  pres- 
ent value  to  the  expected  future  income.     The  property  is  there- 
fore considered  as  having  this  value.     For  this  "  time  difference  " 
in  value  the  rate  of  interest  is  the  measure.     In  the  same  way, 
future  expenses  are  discounted  to  get  net  value. 

The  greater  the  time  interval  between  the  present  moment  and 
a  future  transaction,  the  less  will  be  the  importance  of  this  trans- 
action when  discounted  to  determine  its  present  money  value. 
The  net  capital  value  of  property  is  practically  determined  by 
events  occurring  within  the  next  fifty  years,  not  merely  because 
these  events  can  be  more  accurately  prophesied,  but  through  the 
operation  of  the  factor  of  discount,  based  as  it  is  on  the  laws  of 
compound  interest.  Not  only  are  profits  that  are  deferred  for 
fifty  years  of  little  significance  to  the  investor  (§41),  but  the 
future  values  themselves  are  correspondingly  small  when  viewed 
from  the  present  standpoint.  The  immediate  future  occupies 
the  minds  of  men  and  its  relative  importance  is  mathematically 
expressed  in  discounting  to  obtain  capital  values. 

66.  Effect  of  Rate  of  Interest  on  Capital  Value.  —  The  rate 
of  interest  is  a  barometer  which  measures  the  fluctuations  that 


VALUATION  OF  ASSETS  43 

occur  between  the  relative  values  of  future  and  present  income. 
An  increase  in  this  rate,  or  measure,  increases  the  difference  in 
values  due  to  this  time  element.  The  greater  this  difference,  the 
smaller  will  be  all  capital  values.  A  permanent  doubling  of  the 
rates  of  interest  would  diminish  the  value  of  productive  capital 
to  one-half  its  former  worth.  This  premise  is  based  on  the  eco- 
nomic facts  discussed  in  Articles  60  to  64,  which  refer  value 
directly  to  future  income.  High  rates  of  interest  indicate  risk, 
unsettled  conditions  and  instability  of  character,  and  are  thus 
directly  related  to  influences  tending  to  depress  property  values. 
Low  rates  of  interest  correspondingly  raise  the  capital  value  of 
property,  by  diminishing  the  loss  or  discount  necessary  in  arriv- 
ing at  the  present  value  of  the  future  income. 

67.  Uncertainty  of  Capital  Value.  —  The  premise  that  value 
is  based  wholly  on  future  net  income  is  sometimes  questioned, 
because  of  the  uncertainty  which  surrounds  every  element  of 
future  occurrence.  The  determination  of  value  on  this  basis, 
by  mathematical  deductions,  is  a  guess,  to  the  extent  that  these 
future  elements  are  subject  to  change.  Yet  every  sale  of  prop- 
erty is  the  result  of  a  guessing  contest  as  to  these  future  ele- 
ments, rather  than  a  calculation  of  past  costs.  As  two  minds  are 
better  than  one  and  as  the  guess  is  made  the  basis  of  an  actual 
exchange  of  property,  a  sale  as  soon  as  it  is  effected  becomes  a 
new  indicator  or  basis  for  the  next  guess.  The  uncertainty  of 
future  values  is  identical  in  nature  with  other  risks  incurred  in 
business  and  adds  the  element  of  chance  which  becomes  the  basis 
for  practically  all  forms  of  speculation.  The  difference  between 
"legitimate"  and  "speculative"  value  lies  merely  in  the  degree 
of  uncertainty  surrounding  the  future  conditions  upon  which  the 
guess  as  to  present  value  is  based.  The  value  of  bonds  fluctu- 
ates but  slightly  and  then  only  because  of  changes  in  the  "rate  of 
interest,"  for  the  income  is  fixed  and  secure  and  the  price  or 
value  of  the  bond  is  easily  calculated  mathematically  by  use  of 
the  desired  rate  of  interest  in  discounting  this  income.  By 
contrast,  the  uncertainty  and  fluctuation  in  the  value  of  indus- 
trial stocks  is  due  to  a  corresponding  uncertainty  regarding 
future  dividends. 


44  FOREST  VALUATION 

68.  Independence  of  Capital  Value  and  Past  Outlay  or  Cost. 

It  is  essential  to  thoroughly  establish  the  idea  of  this  inde- 
pendence of  capital  or  expectation  value  from  all  elements  of 
past  cost.  It  cannot  be  said  that  past  costs  are  without  in- 
fluence on  value.  In  most  cases  they  have  been  the  direct  means 
of  creating  this  value.  This  leads  to  the  erroneous  conclusion 
that  such  costs  are  identical  with  value  or  are  value.  The 
fallacy  of  this  idea  is  easily  shown.  Cost  is  an  individual  outlay. 
Value  is  the  product  of  social  conditions.  Costs  are  undertaken 
in  order  to  obtain  value  and,  when  contrasted,  are  negative 
where  value  is  positive. 

To  illustrate:  Two  parcels  of  land  are  acquired  and  cleared 
at  an  expense  in  each  instance  of  $25  per  acre.  One  tract 
has  such  poor  soil  that  it  will  raise  nothing  of  value  and  cannot 
be  sold  for  $5  per  acre.  The  other  is  suitable  for  truck  gar- 
dening and  eventually  sells  for  $500  per  acre.  Such  variations 
in  value,  entirely  independent  of  cost,  may  be  caused  by  differ- 
ences in  location  or  by  the  development  of  new  crops  or  new 
markets.  All  such  fluctuations  are  due  directly  to  the  prospects 
for  future  income. 

The  true  relation  between  cost  and  value  is  that  between  a 
means  and  an  end.  The  cost  is  assumed  for  the  purpose  of 
obtaining  income  and  the  value  is  derived  from  the  prospect 
of  this  income.  If  the  outlay  has  been  effectual  in  insuring 
the  future  income  the  rise  in  value  will  follow.  If  the  outlay 
is  ineffectual  for  any  cause,  chiefly  through  errors  of  judgment 
or  through  incompetence,  there  will  be  no  corresponding  increase 
in  value.  On  the  other  hand,  value  will  increase  and  decrease 
from  social  and  economic  causes  not  even  remotely  associated 
with  the  owner's  outlay.  For  these  reasons  it  must  be  accepted 
that  past  cost  or  outlay,  while  it  may  furnish  useful  information 
for  the  calculation  of  value,  does  not  determine  value. 

69.  Effect  of  Capital  Value   on   Sale   Value.  —  Sale  value 
depends  directly  upon    the   demonstrated  ability  of  property 
to   earn  income.     Whenever   this   earning   capacity  is  uncer- 
tain, especially  if  it  appears  probable  that  it  may  increase  in  the 
future,  sale  values  move  in  response  to  the  guesses  of  those 


VALUATION  OF  ASSETS  45 

who  exchange  property,  as  to  the  probable  future  income. 
Inflated  ideas  of  future  income,  if  commonly  accepted,  result  in 
inflated  sale  values,  as  instanced  in  real  estate  booms,  high 
values  for  western  fruit  lands  and  flurries  in  mining  stocks. 
Could  sound,  reliable  information  regarding  the  possible  future 
income  from  property  be  a  matter  of  common  knowledge, 
inflation  of  values  would  become  very  difficult.  Occasionally, 
by  rapid  development  of  a  region,  values  which  at  first  seemed 
high  materialize  by  the  assurance  of  income  resulting  from 
this  increase  in  population.  More  often  the  boom  is  overdone, 
and  sooner  or  later,  values  collapse  to  a  level  corresponding  to 
the  measure  of  income  possible.  In  every  case  the  sale  value  is 
a  crude  attempt  at  approximating  capital  value,  and  the  disa- 
greement between  them  is  due  to  ignorance  of  the  investing 
public  as  to  the  true  present  value  of  the  possible  income. 

70.  Effect  of  Capital  Value  upon  Appraised  Value.  —  The 
appraiser  must  therefore  take  into  account  the  actual  sources 
of  value  in  appraising  property  in  order  to  check  the  sale  value 
and  detect  any  glaring  discrepancies  between  the   reasonable 
capital  value  of  the  net  income  and  the  price  asked  for  the 
property.     If  the  owners  of  wood  lots  are  selling  their  timber  at 
one-half  to  one-third  of  its  real  value,  because  they  are  ignorant 
of  both  the  quantity  of  standing  timber  they  possess  and  the 
current  prices  for  stumpage,  or  if  these  current  prices  mani- 
festly are  so  low  that  the  purchaser  is  able  to  make  a  very  large 
profit,  the  appraiser  can  go  back  of  sale  values  and  determine 
the  value  of  such  stumpage  directly  from  income  (§  61).    Where 
no  sale  values  exist,  the  determination  of  capital  value  is  his 
only  recourse  and  is  fully  satisfactory. 

71.  Inflation  of  Capital  Values.  —  Value  thus  depends  upon 
future  income  which  may  never  materialize.     On  the  chances 
of  obtaining  this  income,  investors  are  willing  to  purchase  prop- 
erty at  values  computed  by  discounting  these  chances.     The 
rate  of  income  earned  on  the  past  cost  or  invested  capital  of  the 
owner  does  not  fix  the  price  of  the  property.     The  amount  and 
value  of  this  income  are  the  determining  factors.     The  price  is 
determined  by  discounting  this  value,  using  a  rate  of  interest 


46  FOREST  VALUATION 

which  is  satisfactory  to  both  the  purchaser  and  owner.  Should 
a  business  be  sold  which  represents  an  investment  of  $50,000, 
and  earns  a  net  income  of  $25,000  per  year,  or  50  per  cent  on 
cost,  the  purchaser  would  probably  be  satisfied  with  20  per  cent 
per  year.  The  price  will  then  be  -**- — ,  or  $125,000,  and  the 

former  owner  has  exchanged  his  income  of  $25,000  for  capital 
on  which  he  in  turn  must  earn  20  per  cent  in  order  to  be  as  well 
off  as  before. 

In  the  large  operations  of  modern  finance,  especially  in  the 
formation  of  trusts  and  transportation  monopolies,  it  was  con- 
sidered that  unlimited  opportunities  for  future  income  would 
be  created  by  the  control  of  prices  and  railroad  rates.  This 
belief  was  then  capitalized  on  a  generous  scale.  The  final  step 
was  to  sell  these  securities  to  the  public,  thus  realizing,  for  the 
original  owners,  the  capitalized  income  which  had  not  been 
earned.  This  inflated  income  must  now  materialize  or  the 
value  of  these  investments  will  correspondingly  diminish,  as 
has  been  the  case  with  many  such  ventures  in  the  recent  past. 

72.  The   Regulation   of   Capitalization.  —  It   is   possible   to 
prevent  the  fraud  and  burdens  of  over-capitalization  by  giving 
to  states  or  the  national  government  the  power  of  supervision 
over  such  semi-public  operations.     Since  income  is  the  key  to 
capitalization,  the  exaction  of  extortionate  rates  or  prices  should 
be  checked.     Capitalization  may  also  be  regulated  to  conform 
to  the  reasonable  requirements  and  to  the  true  earning  power 
of  the  business.     The  effect  of  such  regulation  will  cause  dis- 
proportionate   differences    between    the    capital    value    placed 
upon  a  business  and  its  actual  cost,  to  shrink  to  reasonable 
proportions,  and  the  balance  sheet  to  show  a  margin  of  profit 
more  in  keeping  with  the  best  interests  of  the  public  from  whom 
must  come  the  income  upon  which  these  values  rest. 

73.  The  Problem  of  the  Balance  Sheet.  —  Accounting  prac- 
tice is  based  on  an  equation  in  which 

goods  or  assets  =  liabilities  +  proprietorship. 
The  left-hand  member  of  this  equation  represents  the  tangible 
and  intangible   assets,  at  book  value,   or  whatever   value  is 


VALUATION  OF  ASSETS  47 

adopted  as  correct  according  to  the  conditions  and  principles 
employed  in  determining  such  values.  Accounts  receivable 
and  debts  owing  to  the  business  are  part  of  the  assets. 

The  right-hand  member  represents  the  capital  paid  in  plus  the 
borrowed  capital.  Debts  owed  by  the  business  and  accounts 
payable  plus  borrowed  funds  constitute  the  liabilities. 

In  balancing  the  equation,  the  "value"  of  assets  is  first 
determined.  The  liabilities  are  rigid,  therefore  the  balance 
represents  the  proprietorship.  When  this  is  originally  expressed 
as  capital  stock,  an  excess  of  value  is  shown  as  surplus,  while  a 
deficit  is  carried  to  the  left  member  to  balance. 

Changes  in  the  status  of  the  business,  which  are  constantly 
occurring,  take  one  of  two  forms;  a  change  in  value  of  capital 
resulting  from  net  income  or  loss,  or  a  change  in  said  value 
independent  of  such  net  income  or  loss.  The  cash  for  the  pur- 
chase of  assets  must  come  either  from  the  proprietors  as  addi- 
tional capital,  or  from  surplus  derived  from  income.  On  the 
other  hand,  sales  are  mere  exchanges,  bringing  in  an  equivalent 
asset  in  cash. 

It  is  evident,  then,  that  the  assets  are  increased  only  by 
Additional  capital  invested  by  proprietors. 
Net  income,  from 

Excess  of  sale  value  over  cost  of  assets. 
Revenue  from  use  of  assets. 
Appreciation  in  value  of  assets. 

The  last  item  is  a  potential  income,  which  may  or  may  not  be 
eventually  realized.     In  the  same  way,  assets  are  decreased  by 
Withdrawal  of  capital  by  proprietors. 
Losses  or  destruction  of  assets  not  insured. 
Dividends. 
Expenses. 

All  items  of  current  income  or  expense  effect  a  corresponding 
change  in  the  net  value  of  the  capital,  but  as  the  balance  sheet 
is  not  usually  made  up  of tener  than  once  a  year,  these  items  are 
carried  in  the  profit  and  loss  account,  and  only  the  surplus  or 
deficit  entered  in  the  balance  sheet. 
The  commercial  balance  sheet  attempts  to  show,  first,  the 


4g  FOREST  VALUATION 

status  of  the  assets,  and  second,  the  relation  existing,  as  a  result 
of  this  status,  between  assets  and  proprietors. 

The  problem  of  the  balance  sheet  lies  in  the  treatment  of 
potential  income,  and  its  effect  on  the  value  of  the  assets.  As 
long  as  the  assets  are  entered  at  cost,  and  income  appears  only 
after  it  has  been  actually  received,  no  potential  or  unearned 
profits  appear  in  the  balance.  On  this  basis,  the  excess  of 
annual  costs  over  annual  income  may  be  added  to  capital  as 
cost  of  assets,  as  is  permitted  in  railroad  construction  (§57),  and 
by  the  government  in  computing  the  income  tax  (§  162).  Un- 
earned interest  on  such  costs  would  be  excluded  in  a  balance 
sheet. 

But  if  the  assets  are  revalued,  at  "actual"  value,  based 
perhaps  on  present  increased  sale  value,  but  due  entirely  to 
increased  prospects  of  income  capitalized  as  expectation  value, 
the  alteration  of  the  value  of  the  assets,  thus  justified,  indicates 
an  apparent  profit  to  the  owners  exactly  equalling  this  increase, 
not  yet  realized  nor  available  for  the  payment  of  dividends. 

Not  only  does  the  balance  sheet  fail  to  distinguish  between 
actual  and  potential  profits,  but  it  entirely  ignores  the  element 
of  time  in  indicating  the  relative  value  of  the  profits  earned, 
compared  with  the  capital  invested. 

The  fundamental  relations  exhibited  in  the  balance  sheet, 
and  its  connection  with  the  profit  and  loss  account,  may  be  set 
forth  in  the  following  framework. 

BALANCE  SHEET 
Assets  Liabilities, 

Proprietorship 


Cash. 
Capital  assets  in 
form  of  goods 
or  property. 
Deficit. 

= 

Capital  paid  in. 
Borrowed     capi- 
tal   or   liabili- 
ties. 
Surplus. 

The  diagram  corresponds  to  an  equation  in  which  the  opposite 
sides  may  show  both  plus  and  minus  items.  A  minus  item,  by 
transfer  from  one  side  to  the  other,  becomes  plus.  The  items 
included  in  each  subdivision  represent  a  separate  equation. 


VALUATION  OF  ASSETS 

CHANGES  IN   STATUS  DURING  YEAR 

I.   CAPITAL  ACCOUNT 

a.   Deductions  from  Capital 

i.   Depreciation 


49 


Losses  not  cov- 
ered by  insur- 
ance. 
Depreciation  in 
value  not  off- 
set by  income 
or     deprecia- 
tion fund. 

= 

Corresponding 
reduction  in 
value  of  pro- 
prietorship 
constituting 
a  loss  of  cap- 
ital or  of  sur- 
plus. 

2.   Withdrawal  of  Capital 

Withdrawal  of 
cash  or  other 
assets  by 
transfer  to 
proprietors. 

- 

Cancellation, 
or  reduction 
in  value    of 
capital 
stock. 

These  withdrawals  may  be  induced  by  the  sale  of  certain  of 
the  capital  assets,  or  by  their  depreciation  in  value.  Instead  of 
creating  a  depreciation  fund,  the  investment  in  a  business  may 
be  steadily  reduced.  This  would  be  the  course  pursued  in 
lumbering,  should  it  be  found  impossible  to  reinvest  the  income 
in  new  timber  stumpage  or  otherwise  continue  the  operation. 
The  cancellation  of  bonds  issued  against  standing  timber  must 
keep  pace  with  the  cutting  of  this  timber. 

b.   Additions  to  Capital 
i.   Additional  Investment 


Purchase  of  ad- 

ditional  as- 

Additional capi- 

sets. 

tal  paid  in. 

Cash. 

2.    Income 

Net      income 

(gross   income 

Depreciation 
fund. 
Increase  of  sur- 
plus. 

= 

minus    annual 
expenses,  in- 
terest and  divi- 
dends)    trans- 
ferred   from 

profit  and  loss 

account. 

FOREST  VALUATION 

3.   Capitalized  Expenses 


Increase  in  book 
value,  i.e.,  in 
cost  of  capital 
assets  already 
owned. 

= 

Additional    capi- 
tal   to   meet 
deficit  caused 
by    excess    of 
expenses    over 
income. 

This  last  transaction  consists  in  marking  up  the  capital  assets 
on  the  basis  not  of  value,  but  of  cost,  to  coincide  with  the  addi- 
tional capital  advanced  to  meet  annual  expenses  in  absence  of 
revenue.  Normally  the  deficit  would  appear  as  such  in  the 
balance  sheet  and  not  in  the  capital  account. 

The  appreciation  in  value  of  capital,  or  unrealized  profits, 
requires  no  corresponding  investment,  and  should  be  distin- 
guished from  increase  in  cost  by  a  separate  account. 

4.   Appreciation  of  Assets 


Appreciation  or 
marking  up  of 

Corresponding 
increase  in 
proprietorship 

value  of  capi- 

representing 

tal  assets. 

potential  prof- 

its. 

II.   PROFIT  AND  Loss  ACCOUNT 

This  account  records  the  cash  outlay  and  income  during  the  year,  and 
its  balance,  indicating  a  net  income  or  deficit,  is  then  transferred  to  the 
capital  account,  and  appears  in  the  balance  sheet. 


4.    Deprecia- 

i.   Cost  of  cap- 

tion fund. 

ital  assets. 

2.   Annual  ex- 

Gross income,  in- 

— 

penses. 
3.    Interest  on 
borrowed 

cluding  sale  of 
capital  assets. 

6.   Additions  to 

capital. 

surplus. 

5.    Dividends. 

Item  i  represents  cost  of  assets  sold,  and  this  amount  is 
credited  to  the  capital  asset  account.  Item  2  includes 
the  current  expenses  of  operation  including  taxes.  Item  3, 
interest  on  borrowed  capital  is  met  before  further  disposition 
of  income  is  permitted.  In  item  4,  the  depreciation  fund  thus 


VALUATION  OF  ASSETS  $1 

appropriated  from  income  offsets  the  loss  from  this  source  in  the 
capital  account.  Item  5,  dividends  are  then  appropriated,  and 
the  remainder  of  the  annual  income  (item  6)  represents  profits 
remaining  in  the  business. 

A  deficit,  instead  of  a  net  income,  occurs  if  the  gross  income 
is  insufficient  to  cancel  the  first  three  items.  When  a  regular 
annual  provision  is  made  for  depreciation  this  may  also  cause 
a  deficit.  In  case  this  deficit  occurs,  it  results  either  in  dimin- 
ishing the  surplus,  or  the  value  of  the  proprietor's  equity,  or 
else  it  is  considered  as  a  natural  and  legitimate  cost  to  be  added 
to  capital  expenditure.  This  difference  in  the  point  of  view 
coincides  with  the  difference  between  enterprises  yielding  annual 
income  and  investments  on  which  income  is  naturally  deferred 
for  longer  periods. 

The  failure  of  the  commercial  balance  sheet  to  fully  inform 
the  investor  as  to  the  true  economic  status  of  his  business,  for 
the  reasons  mentioned  (page  48),  suggests  a  supplementary 
statement,  in  which  the  factor  of  time,  and  the  increase  in  value 
of  assets  due  to  future  or  potential  income,  may  be  expressed. 
Such  a  statement  is  merely  a  prospectus  or  forecast,  but  will  be 
of  great  value  if  its  true  character  is  clearly  explained.  Its 
principal  use  is  found  in  connection  with  a  business  in  which  the 
actual  returns  are  deferred  rather  than  annual. 


III.  PROSPECTUS  OR  FORECAST 


Debit 


Credit 


Expectation 

Total  cash  in- 

value of  future 
income,    capi- 
talized as  val- 
ue of  assets. 

Future  costs  to 
be  subtracted 
from  income 
previous  to 

= 

Past  income. 
Interest  cred- 
ited on  past 

vestment  for 
all  purposes. 
Interest  defer- 
red on   cash 

capitalization. 

investment. 

Potential  profit. 

Potential  loss. 

To  obtain  this  last  balance,  the  cost  of  assets  must  be  shifted 
to  the  "credit"  column,  thus  comparing  cost  with  capitalized 
or  expectation  value  and  revealing  the  potential  profit  by  which 
the  true  economic  status  of  the  business  may  be  gauged. 

The  sources  of  confusion  in  the  treatment  of  assets  by 
accountants  are  now  revealed.  Costs  and  value  are  diametri- 


52  FOREST   VALUATION 

cally  opposite  in  character,  yet  custom  and  the  practical 
necessities  of  commercial  accounting  compel  a  consolidation  or 
compromise  between  these  elements,  as  a  result  of  which  the 
valuation  of  assets  is  sometimes  based  on  cost,  with  or  without 
"  expenses,"  sometimes  on  capital  value,  and  often  on  both 
cost  and  value.  Sprague*  both  sums  up  and  explains  this 
practice  by  the  statement:  "The  aspect  of  assets  as  the  present 
worth  of  future  services  (capitalized  income)!  is  entirely  based 
on  opinion,  while  the  aspect  which  regards  them  (assets)  as  the 
resultant  of  services  (cost)  is  based  upon  facts." 

It  is  evident  that  the  proprietor  is  at  liberty  to  compute  his 
potential  profits  by  capitalizing  future  net  income  on  any  basis 
which  he  sees  fit,  and  may  charge  against  this  value  a  cost  on 
which  he  adds  the  unearned  interest  on  his  capital.  He  may  in 
this  manner  satisfy  himself  as  to  his  economic  status,  and  deter- 
mine whether  to  sell,  buy,  or  continue  to  operate.  But  in  public 
accounts  a  limit  must  be  placed  both  upon  inclusion  of  costs 
not  actually  incurred,  and  of  profits  not  yet  realized.  Hence 
the  full  and  perfect  expression  of  economic  status  is  seldom  per- 
mitted or  secured  by  the  commercial  balance  sheet,  and  must 
be  left  to  supplementary  calculations  in  the  nature  of  forecasts. 

In  this  economic  comparison,  the  proprietary  or  right-hand 
member  of  the  ordinary  balance  sheet  does  not  appear,  and  the 
account  deals  entirely  with  the  material  assets.  The  balance 
is  struck  between  past  costs,  with  interest,  less  past  income, 
and  future  value,  discounted,  less  future  expenses.  Instead  of 
being  upon  the  same  side  of  the  equation,  necessitating  an 
arbitrary  choice  between  absolutely  opposite  elements,  the 
equation  lies  between  cost  and  value,  and  the  balancing  quantity 
is  the  potential  or  unearned  profit  or  loss,  expressed  as  capitalized 
or  expectation  value. 

The  incorporation  of  a  portion  of  this  potential  profit  into 
the  regular  balance  sheet,  previous  to  actual  sale  of  the  business, 
is  an  action  dictated  entirely  by  motives  of  expediency. 

*  "  The  Philosophy  of  Accounts,"  by  Charles  E.  Sprague,  54  West  32d  St.,  New 
York,  p.  41,  Art.  in.     Published  by  author  (at  above  address).     1908. 
t  Material  in  parentheses  inserted  by  author. 


CHAPTER   V 
FORMULAE    OF   COMPOUND   INTEREST 

74.  The  Discount  Factor.  —  The  mathematical  relation  be- 
tween present  and  future  values  is  expressed  by  formulae.     By 
substituting  the  desired  rate  of  interest  in  the  formula  the  ratio 
is  found  by  which  the  one  value  may  be  converted  into  the  other. 
This  ratio  may  be  termed  the  "discount  factor." 

75.  Rentals.  —  The    term    "rental"   is    used    to    denote   a 
definite   sum   recurring  as  income  at  regular  intervals.     The 
interval  may  be  of  any  length,  even  one  hundred  years,  provided 
the  payment  is  assumed  to  recur  periodically.     Since  income 
to  one  person  means  outlay  to  another,  the  amount  of  an  expense 
occurring  at  regular  periods  is  obtained  by  treating  it  as  a  rental. 
The  sum  of  the  future  values  of  a  series  of  payments  consti- 
tuting a  rental  must  frequently  be  determined,  as  well  as  the 
discounted  or  present  value  of  this  sum. 

The  formulas  needed  in  valuation  are  those  which  will  deter- 
mine : 

The  future  value  of  single  sums. 

The  present  value  of  future  sums. 

The  future  value  of  the  sum  of  rentals. 

The  present  value  of  the  sum  of  future  rentals. 

The  ratio  between  present  and  future  values. 

76.  Future  Value  or  Cost  of  Single  Sums.  — 

V  =  value  of  capital  or  sum. 
VQ  =  value  at  beginning  of  period. 
Vn  =  value  at  end  of  period. 

Vi,  Vz  =  value  at  end  of  years  indicated  by  numeral. 
n  =  period  intervening  before  final  reckoning. 
p  =  rate  of  interest  adopted. 


W.W^Xj      J.J.J.  IVslV/Ol,     V/AJJ 

53 


=  o.op,  interest  expressed  decimally. 
100 


54 


FOREST  VALUATION 


The  expression  o.op  is  an  arithmetical  term,  in  which  the  letter 
p  is  substituted  for  the  numeral  representing  the  rate  of  interest. 
For  a  given  rate,  as  4  per  cent,  the  expression  reads  0.04;  for  10 
per  cent,  it  reads  o.io. 

o.op  is  the  ratio  between  capital  and  interest  for  one  year. 
Therefore  i  +  o.op,  or  i  .op,  is  the  ratio  between  the  capital  at 
the  beginning  and  end  of  the  year,  assuming  that  the  interest  is 
added  to  the  principal. 

7i:P0::i.o£:i. 

Vi  =  V0  X  i. op. 

At  the  end  of  the  second  year 

F2  :  Vi  :  :  i.op  :  i. 
F2  =Vi  X  i. op 

=  (Fo  X  i  .op)  i. op 

=  Fo  X  i.of, 
Vz=  (V0X  i. op2)  i. op 

=  Fo  X  i. of 
and  Vn=  (Fo  X  i.op^  i.op 

=  Fo  X  i. op".  (I) 

This  formula  is  used  to  determine  the  accumulation  of  cost  on 
an  investment  which  does  not  produce  income  until  the  close  of 
a  stated  period.  In  such  a  cost  account  (§§  25  and  36)  all  in- 
vestments are  charged  with  interest.  Sums  representing  expend- 
itures which  occur  only  once  and  cannot  be  treated  as  rentals, 
as,  for  instance,  the  cost  of  planting  trees,  are  totalled  for  n 
years  by  this  means. 

All  formulae  dealing  with  future  values  of  present  sums  show 
also  the  present  cost  of  past  expenditures.  They  reckon  forward 
from  beginning  to  end  of  an  investment. 

77.  Present,  Expectation,  or  Capital  Value  of  Future  Sums.  — 
In  computing  future  sums,  the  value  at  a  future  period  has  no 
special  significance  until  it  is  discounted  to  the  present. 

If  Vn  =  Fo  X  i.opn 

then  VQ  =         n.  (II) 


FORMULAE  OF   COMPOUND  INTEREST  55 

The  arithmetical  equivalent  of  — l—^  may  be  expressed  as  a 

decimal. 

Discount  formulae  are  used  in  valuation  of  assets.  The 
discounting  of  future  "profits"  or  net  income  is  identical  with 
the  determination  of  capital  value.  There  can  be  no  value  in 
excess  of  this  discounted  net  income  (§  62). 

To  obtain  this  net  present  value,  future  costs  may  be  first 
discounted  and  then  subtracted  from  discounted  gross  income. 
Or  this  subtraction  may  be  made  at  any  future  period  and  the 
net  income  discounted.  If  the  values  are  properly  computed 
to  the  same  year,  before  striking  the  balance,  the  discounted 
results  are  identical.  For  instance,  an  expense  c  occurs  in  the 
year  d,  which  lies  between  the  years  o  and  n. 

The  present  value  or  equivalent  of  c  will  be • 

i. op 

The  future  equivalent  of  c  at  the  end  of  the  year  n  will  be 
c  X  i.opn~d,  since  n  —  d  is  the  period  over  which  interest  on  c 
would  accumulate. 

The  present  equivalent  of  c  X  i.opn~d  will  be 
c  X  i.opn-d 
i.opn 

Hence,  to  determine  the  net  present  value  of  future  income, 
future  expenses  may  be  computed  forward  to  the  year  in  which 
the  income  is  received,  and  subtracted  from  this  income,  and  the 
resultant  net  income  discounted  to  the  present.  This  accom- 
plishes the  same  purpose  as  discounting  each  item  of  expense 
to  the  present  before  subtracting  it  from  gross  income.  The 
choice  of  these  methods  is  merely  a  matter  of  convenience. 

78.  Use  of  Logarithms  and  Tables.  —  The  arithmetical 
equivalents  of  these  formulae  are  calculated  by  the  use  of  loga- 
rithms. The  numeral  representing  the  desired  rate  of  interest 
is  substituted  for  p,  and  the  number  of  years  in  the  period  for 
n.  For  4  per  cent  and  50  years,  i.opn  becomes  z.0450.  The 
logarithm  of  i  .04  is  multiplied  by  50.  The  result  is  the  logarithm 
of  z.0450,  from  which  the  ratio  is  obtained.  In  the  case  cited, 
the  ratio  is  7.1067,  which  indicates  that  $1.00  will  increase  in 


56  FOREST  VALUATION 

value  to  $7.1067  if  placed  at  compound  interest  at  4  per  cent  for 
fifty  years. 

The  value  of  all  other  formulae  are  derived  from  the  expression 

i.opn.    The  values  for  discount, ,  are  obtained  by  reducing 

the  fraction  to  a  decimal.      In  the  above  case,  —    —  gives  a 

7.1067  fe 

discount  factor  of  0.1407,  which  means  that  $1.00  payable  in 
fifty  years  has  a  present  value,  at  4  per  cent,  of  $0.1407. 

These  values  may  be  expressed  in  tables,  which  make  such 
calculations  unnecessary.  (Table  VI,  appendix.) 

79.  Future  Value  of  Temporary  Annual  Rentals.  —  The 
future  value,  or  cost,  of  a  rental  continuing  for  a  temporary 
period  represented  by  n  annual  payments,  equals  the  sum  of 
all  these  items  plus  interest  upon  each  from  the  date  of  pay- 
ment to  the  end  of  the  year  n. 

The  payments  are  regarded  as  occurring  in  each  instance  at 
the  end  of  the  year,  although  they  might  be  made  during  the 
year.  The  final  payment  thus  incurs  no  interest  charge. 

Let  r  =  annual  rental. 

Then,  final  rental  for  year  n  =  r. 

Rental  for  year  n  —  i,  in  year  n     =  r  X  i.op. 

Rental  for  n  —  2,  in  year  n  =  r  X  i.op2. 

Rental  for  first  year,  in  year  n        =  r  X  i.opn~l. 

These  terms  form  an  increasing  series  showing  a  geometrical 
progression.  The  ratio  of  increase  or  multiple  is  the  factor  i.op. 
The  sum  of  these  terms  gives  the  total  value  or  expense  of  the 
rental  at  the  end  of  the  period.  The  calculation  of  these  separate 
values  is  unnecessary.  The  sum  may  be  obtained  by  formula. 

Let  Fr  =  total  value  of  rental. 

(1)  Fr=r  +  r(i.o/0+r(i.o/>2)+r(i.o/>3)+.  •  •  +r(i.o/>"-1). 
Multiply  the  equation  by  the  ratio  i.op. 

(2)  Vr(i.op)  =  r(i.op)+r(i.of)+r(i.of)-\ \-r(i.opn}. 

Subtract  (i)  from  (2). 

Vr(i.op)-  Vr=r(i.opn)-r, 
Vr(i.op-  i)  =r(i.opn-  i), 

rr_;.(i.o/>n-i), 
i.op  —  i 


FORMULA  OF  COMPOUND  INTEREST  57 

Since          i.op  —  i  =  o.op, 

Fr_r(..or-.) 

o.op 

'-(i-opn  -  i). 
o.op 

Outlay  for  fire  protection  or  sums  paid  annually  for  adminis- 
tration serve  as  examples  of  annual  rentals.  As  income  we  may 
have  receipts  from  grazing  or  hunting  privileges.  The  above 
formula  holds  good  only  during  the  period  that  such  rentals 
remain  equal  in  amount  and  value  as  is  the  case  with  actual 
rent.  Should  they  fluctuate  annually,  each  item  must  be  sep- 
arately computed. 

If  rentals  remain  the  same  for  a  period  and  then  rise  or  fall 
to  a  different  level  for  a  second  period,  the  above  formula  is 
used  to  compute  the  total  to  the  end  of  the  first  period.  This 
value  then  bears  interest  for  the  remaining  period  as  a  definite 
sum  (I),  and  the  value  of  the  new  rental  r\  for  this  second 
period  is  computed  in  the  same  manner  as  before  and  added  to 
the  total.  For  two  periods  termed  a  and  b  this  reads: 


_ 


o.op         )  o.op 

80.  Formulae  for  Geometric  Series.  —  In  the  series  whose  sum 
is  obtained  by  Formula  III,  the  ratio  i.op  is  greater  than  i, 
which  gives  an  increasing  series. 
Let  g  =  first  term  of  series. 

q  =  ratio  or  multiple  (such  as  i.op). 
Q  =  sum  of  series. 
Then,  by  demonstration  above  (III), 


The  sum  of  future  values  of  rentals  forms  such  a  series. 

Should  the  ratio  be  less  than  i,  each  succeeding  term  will  be 
diminished  in  value,  which  gives  a  decreasing  series. 

The  sum  of  this  series  is  obtained  by  the  same  formula,  but 
a  more  convenient  form  of  expression,  obtained  by  multiplying 
both  numerator  and  denominator  by  —  i  ,  is 


(Q,) 


58  FOREST  VALUATION 

The  sum  of  present  or  discounted  values  of  rentals  forms  such 
a  descending  series. 

These  formulae  apply  either  to  temporary  rentals,  with  a 
limited  number  of  terms,  or  to  perpetual  rentals,  with  an  infinite 
number  of  terms. 

For  an  in  finite  increasing  series 

Q  =  s(f       -  =  x  (infinity).  (Q,) 

q  -  i 

For  an  infinite  decreasing  series,  since  the  value  of  $•*  dimin- 
ishes in  direct  proportion  to  the  exponent  used, 

f  =o. 
Therefore 


81.  Present,  Expectation,   or   Capital   Value   of   Temporary 

Annual    Rentals.  —  Let    R  =  present,   expectation,    or   capital 
value  of  the  sum  of  a  rental. 

Should  each  rental  be  discounted  to  the  present  by  Formula 
I,  the  sum  of  the  reuniting  terms  is 


i.op      i.op2  '   i.op3  '   i.op*' 

Applying    Formula    Q.    for    the    summation    of    decreasing 
temporary  rentals. 


,.,       i.op  i.op1 

K  =  ——«—————* . 

i.op 
Multiplying  numerator  and  denominator  by  i.op  X 

R  =     rd.op*  -  i) 
(i.op  —  i)  i.op* 


o.op  X  i.op* 


(iv) 


FORMULA  OF   COMPOUND  INTEREST  59 

The  same  result  may  be  obtained  by  discounting  the  final 
future  value  of  the  sum  of  these  rentals  to  the  present  (II). 


This  future  value  Vr  = 


O.Qp 


Hence  r(i.opn  —  i)  i       _  r  (i.oft*  —  i) 

o.op  i.  op*       o.op  X  i.  op* 

Since  capital  value  is  the  net  value  of  income  discounted  to 
the  present,  the  application  of  this  formula  is  evident.  It  may 
be  used  to  discount  either  annual  income  or  annual  expenses. 
Should  the  two  occur  simultaneously,  only  the  net  annual 
profit  or  loss  is  thus  discounted. 

82.  Future  Value  of  Temporary  Intermittent  Rentals  Due 
First  at  n  Years,  and  t  Times  at  Intervals  of  n  Years  There- 
after. —  A  rental  which  occurs  at  intervals  greater  than  one 
year  is  termed  intermittent,  although  if  the  interval  is  regular 
it  does  not  differ  in  character  but  only  in  degree  from  annual 
or  monthly  rentals. 

Let         n  =  period  between  rentals. 

/  =  number  of  payments  expected. 
nt  =  total  period  covered  by  the  investment. 
/  =  intermittent  rentals  due  at  intervals  of  «  years. 
Vr  =  total  value  of  intermittent  rentals  at  end  of  period. 

The  future  value  of  the  sum  of  these  rentals,  if  computed  in 
the  year  of  payment  of  the  final  rental,  is 
Final  payment  =  /, 

Payment,  n  years  preceding     =  /  (i.op*), 
Payment,  2  n  years  preceding  =  /  (i.o/^2"), 
First  payment  =  /  (i  .o^*-^  "). 

By  use  of  Formula  Qi,  the  sum  of  these  terms  is  found  by 
substituting  the  ratio  i.opn  for  q  and  the  factor  t  for  n. 
The  formula  then  reads: 

>.  (V) 

Either  income  or  expenses  which  terminate  at  a  definite 
date  are  far  more  apt  to  occur  annually  than  at  longer  intervals 


60  FOREST  VALUATION 

(III  and  IV),  and  if  intermittent  and  terminating,  such  as  a 
succession  of  thinnings  from  a  crop  of  timber  previous  to  final 
cutting,  they  are  also  apt  to  be  of  different  values,  requiring 
separate  valuation.  If  assumed  to  be  equal  in  value,  they  may 
usually  be  assumed  to  recur  perpetually  (IX). 

83.  Present,  Expectation,  or  Capital  Value  of  Temporary  Inter- 
mittent Rentals,  Due  First  at  n  Years,  and  t  Times  at  Intervals 
of  n  Years  Thereafter.  —  The  present,  expectation,  or  capital 
value  of  intermittent  rentals  limited  in  number  is  found  as 
in  the  case  of  annual  rentals. 

The  series  decreases. 

For  rentals  due  first  after  n  years  and  t  times  at  intervals  of 
n  years  thereafter,  this  series  is 

R=-^  +  ^-  +  -^-+  -  |       r' 

i.opn      i.op2n      i.op3n  i.optn 

Then  (Q2), 


Q=1-^- 


i.opn 

i 
i.opn 

i.opnt) 


I 
I  — 


i.opn 
Multiplying  numerator  and  denominator  by  i.opn  X  i.opnt, 

R_       /d.O^-1) 

(i.opn  -  i)  i.opnt 
The  same  result  is  obtained  by  discounting  the  future  value 

of  the  series  (V)  to  the  present  (II)  using  the  factor  — —   as 

i.opnt 

the  substitute  for  — —  • 
i.opn 

R  =  r'  (i.opnt  -  i)  x      i      =     r'  (i.opnt  -  i) 

i.opn  -  i          i.opnt      (i.opn  -  i)  i.opnt' 
84.   Future  Value  of  Temporary  Intermittent  Rentals,  Due 
First  in  a  Years,  and  t  Times  at  Intervals  of  n  Years  There- 
after. —  When  the  value  of  the  sum  of   temporary  rentals  is 


FORMULA  OF  COMPOUND  INTEREST  6l 

determined  for  the  date  of  the  final  payment,  falling  in  the 
year  nt,  the  interval  elapsing  subsequent  to  this  payment  is 
zero.  When  this  payment  falls  at  some  previous  date,  a,  the 
total  value  at  that  date  accumulates  interest  during  the  remain- 
ing period.  This  period  is  equal  to  n  —  a  years. 
The  series  forming  the  sum  of  the  rentals  is 

Vr   =   /  (l.O/>»-°)    +  /  (l.O/"-°)     '     •     •      +  /  (l.<tf"~). 

By  use  of  Formula  Qi,  substituting  the  ratio  i.opn  for  q,  and 
the  factor  t  for  n,  this  becomes 


_ 


i.opn  - 

By  multiplying  Formula  V  by  i.opn~a  (see  Formula  I),  the 
same  result  is  obtained. 

85.  Present,  Expectation,  or  Capital  Value  of  Temporary 
Intermittent  Rentals,  Due  First  in  a  Years,  and  t  Times  at 
Intervals  of  n  Years  Thereafter.  —  The  present  value  of  the 

first  payment,  due  in  a  years,  is  —  —  (II)  .  The  period  a  may  be 
of  any  length  and  may  exceed  n.  The  present  value  of  subse- 
quent payments  diminishes  by  the  constant  ratio  —  —  ,  form- 
ing the  series 

r'         r' 

I 


i.opa      i.opa+n       i.o/>a+2n 
To  obtain  the  sum  of  present  values  (Q2), 


g  = 


i.opa 

i 


i.opn 

-U- 


i.opa\        i.opntJ 
*  i 

i.opn 

I.O/>° 


62  FOREST  VALUATION 

Multiplying  numerator  and  denominator  by  i.opn  X  i.o/>n<, 

Jt_/(.^--.)..or-. 

(i.opn  —  i)  i.opn 
This  formula  is  also  derived  from  Formula  VII  by  discounting 

the  final  value  to  the  present  (II),  substituting  —     —  for — —  • 

i.opnt        i.opn 

Formulae  V  to  VIII  are  seldom  used  in  forest  valuation 
(§82). 

86.  Present,  Expectation,  or  Capital  Value  of  Perpetual 
Rentals.  —  Under  the  assumption  that  a  rental  is  perpetual 
(§80),  the  intermittent  rental  r,  payable  every  n  years,  forever 
will  have  a  future  value  equal  to  infinity  (oo). 

Its  present  value  (Q4)  is 


(IX) 

If  the  first  rental  is  paid  in  the  year  a  instead  of  at  n  years, 
as  in  case  of  revenue  from  thinnings,  the  present  value  of  the 
sum  of  a  perpetual  series  due  every  n  years  thereafter  (Q4)  is 

g  ~  i.opa' 
i 


FORMULA  OF  COMPOUND  INTEREST 


But  should  the  period  of  discount  lie  between  the  year  a  and 
the  final  year  n,  when  the  crop  is  harvested,  as  it  does  when 
the  value  of  growing  timber  is  computed  at  a  years,  this  formula 
(Q4)  is 


g  = 


i.opn~ 

I 

i.opn' 
r' 


R  = 


i.opn  — 


(Xa) 


When  the  first  rental  is  due  in  the  present  year,  the  series 
becomes 


R  = 


i.opn  — 


(XI) 


By  separating  the  first  payment  from  the  series,  the  remaining 
terms  equal  ;       -  (see  IX),  and  the  sum  is 


i.opn  — 


r' 


(XIa) 


i.opn  —  i 

An  annual  rental,  payable  perpetually,  has  a  present,  expecta- 
tion, or  capital  value  (Q4)  of 

r 
i. op' 

i 


8  — 
2 


i. op 


64 


R  = 


i.  op  —  i 


o.op 

Formulas  IX  to  XII  are  of  great  importance  in  forest  valuation. 
The  conception  that  a  rental  may  be  perpetual  is  difficult  to 
grasp.  But  this  is  merely  another  way  of  stating  that  the  prop- 
erty producing  the  rental  does  not  depreciate  in  value.  Grant- 
ing this  premise,  the  receipt  of  income  for  any  given  period 
leaves  the  property  capable  of  yielding  another  return  of  equal 
value.  Since  this  assumption  can  be  extended  indefinitely,  the 
expected  income  may  be  regarded  as  perpetual. 

Formula  XII  is  customarily  used  to  determine  the  money 
capital  which  will  produce  an  annual  income  of  r.  If  we  assume 
that  money  remains  of  the  same  value,  and  nothing  occurs  to 
impair  the  integrity  of  the  capital,  it  can  be  imagined  that 
this  income  is  perpetual.  In  the  case  of  land  whose  fertility  is 
maintained  by  proper  methods,  so  that  the  net  income  does 
not  represent  a  drain  of  capital,  or  soil  depreciation,  the  same 
conditions  are  true,  and  the  capital  value  of  the  soil  may  be 
found  by  use  of  Formula  XII. 

This  premise  will  hold  for  forest  lands  producing  crops  at 
long  intervals.  The  trees  maintain  the  productiveness  of  the 
soil.  In  this  case,  the  net  income,  being  intermittent,  is  cap- 
italized by  Formula  IX. 

For  practically  all  other  forms  of  investment,  revenue  is 
apt  to  be  accompanied  by  depreciation  of  capital,  which  causes 
the  income  to  diminish  and  finally  terminate,  thus  requiring, 
instead  of  the  simple  formulae  just  quoted,  the  use  of  the  formulae 
IV,  VI  or  VIII  for  the  present  value  of  temporary  rentals. 

These  values  are  less  than  those  obtained  by  -  -  -  or  —  ^- 

i.opn  —  i       o.op 


FORMUL/E  OF   COMPOUND   INTEREST  65 

and  the  erroneous  use  of  these  latter  formulae  leads  to  over- 
valuation of  assets. 

87.  Relation  Between  Future  Value  of  Temporary  Annual 
Rentals   and   Present,    or   Capital,  Value   of   Same.  — In  the 

formula  for  future  value  of  temporary  annual  rentals,  expressed 

as  — ^—  (i.opn—  i)  (§7 9),  the  portion represents  the  capital 

o.op  o.op 

value  of  a  perpetual  annual  rental  (XII),  or  the  capital  which 
will  produce  an  annual  income  of  r.     This  formula  might  be 

expressed (i.opn) :—  • 

o.op  o.op 

Substituting  R  for > 

o.op 

R  =  capital  value  of  annual  rental  r. 

Then  —  (i.opn) —  =  R  X  i.op"  -  R 

o.op  o.op 

=  R(i.opn  -  i).  (Illb) 

This  expression  gives  the  sum  of  the  compound  interest,  or 
deferred  income,  earned  by  the  capital  R  in  n  years,  and  is 
obtained  by  computing  the  value  of  R  at  n  years  at  p  per  cent, 
and  then  subtracting  the  original  capital. 

The  numeral  i  substituted  for  R  indicates  that  at  any  future 
period  the  original  capital  remains  intact.  Since  the  sum  of 
the  future  values  of  an  annual  rental  is  thus  shown  to  equal 
the  compound  interest  or  income  on  its  capitalized  value,  the 
formula  R  (i.opn  —  i)  may  be  used  to  compute  the  total  cost 
not  only  of  annual  rentals,  but  of  interest  on  invested  capital 
whenever  the  capital  so  invested  remains  intact  at  the  end  of 
the  period,  as  is  the  case  with  land. 

88.  Conversion  of  Intermittent  into  Annual  Rentals.  —  To 
convert  an  intermittent  rental  occurring  every  n  years  into  its 
equivalent  annual  rental,  it  is  incorrect  to  divide  the  amount 
of  the  intermittent  rental  by  the  factor  n.     The  intermittent 
rental  is  not  received  until  n  years  from  date,  while  the  annual 
rental  is  received  in  installments  over  the  entire  period,  which 
makes  the  average  period  of  deferred  payment  less  than  half 
as  long. 


66  FOREST  VALUATION 

The  capital  value  of  an  intermittent  rental  is  —          —  and 

i.opn  —  i 

of  an  annual  rental  —  —  .     Since  the  annual  income  for  each  is 
o.op 

required  to  be  equal,  these  expressions  must  have  the  same  value. 


If 


i.  op"  —  i      o.op 
then  r  =  ^      '  _-  X  o.op.        (XIII) 

The  annual  rental  equivalent  to  an  intermittent  rental  falling 
due  first  at  an  interval  shorter  or  longer  than  n  is  found  in 
the  same  way  by  multiplying  the  capital  values  given  in  for- 
mulae XI  and  XII  respectively  by  o.op.  The  results  show  that 
notwithstanding  the  fact  that  the  intermittent  rentals  are 
equal  in  amount  and  paid  at  equal  intervals,  the  capital  value, 
and  its  equivalent  in  permanent  annual  income,  constantly  rises 
until  one  of  the  intermittent  payments  is  received,  which  at 
once  diminishes  this  capital  value  by  the  exact  amount  of  the 
payment.  If  exchanged  for  an  annuity  at  this  time,  the  per- 
manent income  thus  secured  is  the  lowest  for  any  portion  of 
the  period,  while  a  similar  exchange  effected  just  previous  to 
receipt  of  intermittent  income  secures  the  maximum  annual 
revenue. 

89.  The  Ratio  of  Income  or  Earnings.  —  The  "rate  of  inter- 
est," p  per  cent,  is  accepted  as  a  fixed  standard  in  computing 
cost  (I);  or  in  discounting  for  value  (II).  But  when  both  cost, 
or  investment,  and  income  are  known,  the  ratio  of  this  income 
to  cost  represents  the  earnings  of  the  capital  invested,  or  divi- 
dends. A  rate  of  interest  can  be  found  by  which  the  discounted 
value  of  income  is  made  to  exactly  equal  cost,  or  the  accumu- 
lated costs  to  just  balance  income.  This  rate  is  the  per  cent 
earned  by  the  investment. 

To  distinguish  this  rate  from  the  "rate  of  interest"  p,  the 
term  x  will  be  used. 

x  =  per  cent  representing  income  earned. 


FORMULA  OF   COMPOUND  INTEREST  67 


v 

Then  i.oxn  =  - 


i.  ox  =  i  +  o.ox, 

i  +  o. 


0.0*  =  VT7-1. 

(XIV) 


The  rate  x  enables  the  owner  to  compare  the  earning  power 
of  his  investment  with  enterprises  which  produce  annual  divi- 
dends (Chapter  VIII). 

Instead  of  solving  the  above  equation,  the  value  of  x  may  be 
found  by  inspection  of  Table  VI.  The  value  of  i.oxn  is  calcu- 
lated, and  the  nearest  equivalent  figures  must  be  found  opposite 
n  years  in  the  table.  By  interpolation,  x  may  then  be  found  to 
within  one-tenth  of  i  per  cent. 


CHAPTER    VI 
INVESTMENTS  AND  COSTS  IN  FOREST  PRODUCTION 

90.  The  Business  of  Forest  Production  versus  Lumbering.  — 

Lumbering  is  a  term  applied  to  that  portion  of  the  business 
of  forest  utilization  which  begins  with  the  removal  of  the  forest 
products  from  the  soil  and  is  completed  when  the  wood  is 
placed  upon  the  market  as  lumber,  ties,  shingles  or  other  products. 
The  stage  dealing  with  the  felling  and  transportation  of  the  raw 
product  to  place  of  manufacture  is  termed  "logging,"  while  the 
manufacture  itself  is  spoken  of  as  "milling." 

Forest  production  is  a  separate  undertaking,  which  precedes 
lumbering,  and  deals  entirely  with  the  growing  of  forest  crops, 
principally  wood  products.  Until  recently,  the  raw  material 
on  which  the  enormous  investments  in  logging  and  milling  are 
dependent,  was  drawn  entirely  from  virgin  stands  grown  with- 
out human  aid  or  expense.  Ultimately,  forest  production  must 
rank  in  importance  with  lumbering,  for  under  modern  condi- 
tions, forests  will  seldom  renew  themselves  unaided.  The  only 
large  and  complete  organization  of  forest  production  as  a  business 
in  this  country  at  present  is  found  in  the  administration  of  the 
national  forests.  The  operations  of  certain  states  are  gradually 
taking  on  a  systematic  form.  But,  as  a  whole,  the  productive 
side  in  the  management  of  private  timberlands  has  not  yet 
been  organized  into  a  systematic  effort,  and  takes  the  form  of 
tentative  or  experimental  measures,  completely  overshadowed 
by  the  operations  of  lumbering. 

Logging  and  milling  are  indispensable  adjuncts  to  production, 
but  without  it  they  are  self-destructive.  These  three  operations 
complete  the  chain  of  effort  by  which  the  income  from  forestry 
is  finally  secured.  Owners  of  large  tracts  of  timber  usually 
undertake  to  log  them  in  order  to  produce  income  from  their 
holdings,  and  professional  lumbermen  prefer  to  own  their  stump- 

68 


INVESTMENTS  AND  COSTS  IN  FOREST  PRODUCTION         69 

age.  When  stumpage  is  owned,  logged  and  manufactured  by  the 
same  person  or  corporation,  both  costs  and  net  profits  are  based 
on  the  total  operation.  Frequently  an  owner  of  stumpage  will 
contract  the  logging  and  do  his  own  milling.  Both  logging  and 
milling  may  be  contracted,  the  owner  receiving  the  final  net 
revenue  from  sale  of  lumber.  Or,  the  owner  may  sell  his 
stumpage,  permitting  the  logger  and  mill  man  to  make  what 
profit  they  can.  On  the  books  of  a  firm  operating  with  their 
own  stumpage,  a  technical  separation  of  costs  is  made  between 
stumpage,  logging  and  manufacture.  The  total  profits  as  well 
should  theoretically  be  distributed  between  these  three  depart- 
ments, but  for  practical  purposes  this  is  unnecessary.  Where 
desired,  the  "value"  of  stumpage  is  charged  as  a  cost  against 
logging.  By  increasing  this  value,  logging  costs  are  advanced 
in  the  same  proportion,  and  the  profits  disappear  into  stumpage 
values,  without  in  any  way  altering  their  amount  or  character. 
But  should  stumpage  be  owned  separately,  and  its  sale  constitute 
a  transaction  taking  place  between  different  firms,  the  costs  and 
profits  arising  from  sale  of  stumpage  are  actual. 

Forest  production  as  a  separate  business,  or  even  as  a  separate 
department  of  the  general  business  of  lumbering,  is  completed 
with  the  sale  of  the  timber  or  products  on  the  stump.  This 
separation  from  lumbering  is  illustrated  by  the  operations  of 
the  United  States  Forest  Service,  which  performs  no  part  of 
the  logging  or  manufacturing. 

When  an  owner  of  forest  property  finds  it  necessary  to  engage 
in  logging  and  manufacturing,  he  should  separate  the  costs 
and  profits  of  these  enterprises  from  the  profits  on  growing  or 
holding  his  timber.  Often  the  owner  is  in  position  to  log  his 
own  timber.  Th'is  may  result  in  securing  a  combined  or  total 
profit  far  in  excess  of  the  receipts  obtainable  from  sale  of  stump- 
age.  In  general,  lumbering,  to  pay  as  an  enterprise,  requires 
large  tracts  and  a  supply  of  timber  which  will  last  for  a  reason- 
able period,  and  the  owners  of  small  tracts  must  either  sell 
their  timber  on  the  stump  or  contract  for  its  manufacture. 

91.  Proprietary  Accounts  in  Forestry. — Proprietary  accounts, 
showing  the  amount  of  capital  invested,  and  the  income  and 


7o 


FOREST  VALUATION 


outlay,  or  profit  and  loss  in  the  business  of  forest  production,  will 
deal  with  the  operations  of  the  owner  as  a  unit,  and  not  with  the 
stand.  If  such  accounts  are  kept  according  to  the  customary 
forms,  only  actual  cash  outlay  or  income  can  be  recorded. 
The  expenditures  might  be  separated  into  capital  account  for 
such  items  as  land,  and  profit  and  loss  for  wages,  taxes  and 
other  current  expenses. 

Unfortunately,  both  for  the  accountant  and  the  proprietor, 
such  a  business  may  fail  to  pay  dividends  for  an  extended  period. 
Whether  it  does  so  or  not  depends  upon  the  condition  of  the 
forest,  for  if  the  timber  is  already  produced  or  grown,  the  income 
is  within  reach.  With  a  young  forest,  or  plantation,  additional 
capital  is  required  to  cover  every  item  of  annual  outlay  in  excess 
of  income.  Since  no  dividends  are  produced,  interest  on  bor- 
rowed capital  increases  at  a  compound  rate,  actually  when  this 
interest  is  also  borrowed  and  paid,  or  by  analogy,  when  its  pay- 
ment is  merely  deferred. 

Unless  this  condition  is  foreseen,  and  the  enterprise  floated 
without  borrowing,  or  the  loan  is  negotiated  on  the  basis  of 
deferred  instead  of  annual  interest,  which  is  not  customary,  the 
proprietor  must  pay  this  interest  or  bankruptcy  ensues.  No 
existing  custom  of  book-keeping  will  permit  the  charging  of 
unearned  interest  as  a  cost  or  actual  expenditure,  unless  it  is 
paid  out  as  above  indicated.  Hence,  in  the  absence  of  borrowed 
funds,  the  accumulating  " costs"  represented  by  deferred  in- 
terest (§  36)  are  not  shown  on  the  books. 

For  a  forest  investment,  representing,  as  it  usually  does, 
timber  in  all  stages  of  growth,  some  capable  of  yielding  income 
at  once,  while  other  portions  require  outlay  for  many  years,  it 
will  be  necessary  to  keep  a  proprietary  account  in  the  usual 
form,  omitting  the  item  of  deferred  interest  on  the  owner's 
capital.  Such  an  account  will  eventually  show  net  profits, 
regarding  interest  as  income  (§37),  but  it  will  not  reveal  actual 
"cost,"  nor  the  profits  of  the  undertaking  (§39)  or  enterpriser's 
gain. 

92.  Cost  Accounts  in  Forestry.  —  A  serious  defect  in  such 
proprietary  accounts  is  that  the  value  of  the  element  of  time  is 


INVESTMENTS  AND   COSTS  IN  FOREST  PRODUCTION        71 

wholly  neglected  (§  n)  and  profits  received  after  many  years  are 
shown  in  amount  only,  as  though  of  equal  value  with  profits 
of  the  year.  In  contrast,  cost  accounts  (§25)  seek  to  eliminate 
such  inconsistencies  and  express  costs  in  their  true  economic 
relation  to  income.  This  is  accomplished  by  the  adoption  of  a 
rate  of  interest  (§§  52  and  53)  by  which  all  expenditures  are  cal- 
culated forward  to  the  year  when  the  income,  for  which  the  cost 
was  incurred,  is  finally  received  (§  23).  In  practice,  a  separate 
cost  account  could  be  kept  for  each  stand,  lot  or  subdivision. 
The  summary  or  total  to  a  given  date  (the  present)  of  these 
accounts  would  reveal  to  the  proprietor  his  exact  investment, 
including  the  "unearned"  interest.  This  summary  should  differ 
from  the  corresponding  items  in  the  proprietary  account  by  just 
the  amount  of  this  interest. 

93.  Investments,  or  Permanent  Outlay.  —  Expenditures  for 
property  of  a  durable  character  in  forestry  are  confined  to  land 
and  to  permanent  roads,  houses,  telephones  or  other  improve- 
ments.    The  original  cost  of  these  may  be  considered  a  capital 
expenditure. 

94.  Expenses,  or  Temporary  Outlay  in  Forestry. — Temporary 
or  current  expenses  would  ordinarily  include  raw  materials  as 
well  as  items  like  wages  (§21).     But  when  wages  are  expended 
on  planting  trees  and  when  the  raw  material  consists  of  stand- 
ing timber,  which  will  remain  as  property  for  a  period  of  years, 
this  treatment  is  open  to  question.     After  the  forest  property 
has  passed  through  its  initial  stage  of  construction,  and  is  pro- 
ducing annual  revenue,  many  items,  such  as  reforestation,  which 
at  first  call  for  an  initial  investment,  can  be  regarded  as  current 
outlay.     In  this  class  will  fall  all  expenses  for  upkeep  of  im- 
provements. 

95.  Land.  —  Land  is  the  one  investment  which  can  be  credited 
as  capital  not  ordinarily  subject  to  depreciation,  and  indispen- 
sable to  forestry.      It  remains  after  the  timber  is  harvested. 
The  purchase  price  of  land  is  the  only  land  value  which  can 
legitimately  be  entered  in  the  cost  account,  and  this  valuation 
can  remain  the  same  as  long  as  the  owner  retains  the  land  for 
forest  production.     A  sale  of  the  property,  terminating  the 


7  2  FOREST  VALUATION 

ownership  and  cost  account,  calls  for  a  revaluation  of  land  (§§  61 
and  62). 

Bare  land  suitable  only  for  forest  crops  does  not  command 
a  high  price  (§96). 

96.  Standing  Timber.  —  By  definition,  real  estate  comprises 
land  and  all  that  stands  thereon.  A  purchaser  of  land  acquires 
all  permanent  improvements.  These  improvements  may  be 
sold  separately,  but  always  with  the  stipulation  that  they  are 
to  be  removed  within  a  given  time. 

Standing  timber  is  part  of  the  real  estate,  and  a  purchase  of 
land  includes  the  timber,  unless  excepted  by  the  owner  subject 
to  removal  by  him.  Timber  stumpage  is  sold  by  the  owner  on 
contract  which  allows  the  purchaser  a  definite  time  for  removal, 
failing  in  which,  the  purchaser,  in  certain  states,*  loses  his  right 
to  the  timber.  These  timber  rights  sometimes  run  for  periods 
of  twenty  years  and  while  in  force  constitute  a  lien  on  the 
property. 

By  the  time  a  crop  of  timber  is  large  enough  to  cut,  its  value 
greatly  exceeds  that  of  the  land.  Virgin  timber,  containing  ma- 
terial of  high  quality,  shows  a  still  greater  excess  of  value  (§  184). 
In  the  past,  lumbermen  were  quite  indifferent  to  land  values, 
regarding  the  title  as  desirable  only  because  it  made  them  inde- 
pendent of  restrictions  as  to  time  and  rate  of  cutting.  What 
they  purchased  was  the  timber.  Yet  timber,  whether  young  or 
old,  is  a  "vanishing"  asset.  It  must  be  converted  eventually 
into  income,  and  is  subject  to  losses.  Owing  to  the  difficulty, 
in  some  cases,  of  distinguishing  between  the  value  of  the  land 
and  of  the  timber,  and  the  great  preponderance  of  the  latter 
value,  the  cost  of  standing  timber  is  usually  regarded  as  a  cap- 
ital expenditure.  Bonds  may  be  issued,  with  this  standing 
timber  as  security,  provision  being  made  to  retire  these  bonds  at 
a  rate  to  more  than  keep  pace  with  the  cutting  of  the  timber. 
Such  bonds  are  in  this  sense  paid  out  of  "capital,"  as  this  "capi- 
tal" is  converted  into  income.  Bonds  could  not  be  floated  on 
timber  which  was  not  about  to  be,  or  in  process  of  being,  cut. 

*  This  subject  has  caused  extensive  litigation,  and  has  resulted  in  conflicting 
practice.  State  supreme  court  decisions  must  be  ascertained  in  each  locality. 


INVESTMENTS  AND  COSTS  IN  FOREST  PRODUCTION    •    73 

97.  Permanent  Improvements  and  Equipment. — On  any  prop- 
erty managed  exclusively  for  forest  production,  and  of  sufficient 
size  to  demand  continuous  care  and  administration,  buildings 
must  be  provided  for  the  permanent  force,  both  officers  and 
laborers,  especially  since  these  tracts  are  not  often  conveniently 
near  towns.     Special  telephone  construction  is  often  required. 
These  are  legitimately  classed  as  capital  expenditures.     Stables, 
draft  animals  and  tools  come  in  this  category,  but  proper  allow- 
ance for  depreciation  must  be  made. 

In  cost  accounts  for  individual  stands,  it  is  proper  to  dis- 
tribute these  overhead  charges  over  the  entire  territory  which 
they  cover,  pro-rating  them  on  a  per  acre  basis.  The  initial 
cost  for  these  items  may  be  included  with  the  cost  of  land  and 
timber.  The  annual  charge  for  upkeep,  or  its  equivalent  in 
depreciation,  must  be  entered  as  a  current  annual  expense  on 
the  same  acreage  basis. 

98.  Roads  and  Transportation  Systems.  —  Lack  of  perma- 
nent roads  or  other  means  of  transportation  is  characteristic  of 
American  forest  conditions.     To  yield  a  steady  income,  a  forest 
must  produce  wood  annually  for  market,  which  requires  the 
transportation  system  to  be  in  continual  repair. 

In  inaccessible  regions,  timber  must  exist  in  sufficiently  large 
bodies  to  justify  construction  of  a  system  of  transportation  for 
its  removal.  The  cost  of  transportation  contains  two  elements: 
first,  cost  of  construction;  second,  cost  of  transport.  Con- 
struction cost,  no  matter  how  cheapened,  cannot  be  reduced 
below  a  certain  limit.  Cost  of  transport  is  lessened  by  improv- 
ing the  means  of  transportation.  When  railroads,  roads  or 
flumes  are  built  for  merely  temporary  use,  the  entire  cost  of 
construction,  as  well  as  transport,  falls  on  the  timber  removed 
at  the  time,  and  is  pro-rated  for  each  unit  of  product  as,  for 
instance,  per  thousand  feet  of  lumber. 

Since  transportation  is  a  feature  belonging  strictly  to  logging, 
it  affects  forest  production  through  its  influence  on  the  value  of 
stumpage.  It  is  the  universal  practice  hi  America  to  allow  the 
cost  of  construction,  as  well  as  transport,  to  fall  upon  the  logger, 
who  takes  it  out  of  the  price  of  stumpage. 


74  FOREST  VALUATION 

In  permanent  forest  property,  this  construction  cost  may  be 
assumed  by  the  forest  owner,  whether  or  not  he  intends  to  do  the 
logging.  This  is  necessary  in  order  to  permit  of  the  radical 
change  in  logging  from  the  removal  of  practically  the  entire 
crop  at  one  time  to  the  system  of  continuous  removal  of  smaller 
quantities  over  the  entire  area.  Under  the  latter  system,  no 
logging  contractor  could  afford  to  construct  his  own  transpor- 
tation facilities. 

Such  permanent  systems  are  a  capital  expenditure  similar 
in  character  to  land,  and  the  overhead  costs  thus  incurred 
should  be  pro-rated  by  area  and  charged  as  an  addition  to  the 
cost  of  acquiring  the  property.  The  maintenance  of  transpor- 
tation systems  is  an  annual  expense  to  be  pro-rated  in  the  same 
way.  The  owner's  benefit  from  thus  assuming  costs  belonging 
to  logging  is  obtained  by  appropriating  a  larger  share  of  the 
general  profits  through  increased  value  of  stumpage. 

99.  Silvicultural  Operations.  —  All  labor  expended  directly 
upon  the  forest  crop  constitutes  a  charge  against  the  particular 
area  or  stand  which  is  benefited.     Such  costs  include  planting, 
with  the  cost  of  the  plants;    weeding  or  removal  of  injurious 
"weed"  trees  or  brush  when  the  plantation  is  young;  protection 
from  insects  by  measures  requiring  expenditure  of  labor  on  the 
area;  and  thinning,  provided  this  is  done  at  a  cost  exceeding 
the  value  of  the  product  obtained.     Costs  incurred  in  natural 
reproduction,  by  leaving  a  portion  of  the  stand  to  serve  as  seed 
trees,  correspond  to  the  cost  of  planting  and  should  be  charged 
against   the   new   crop.     Practically   all   silvicultural   expenses 
occur  as  single  or  initial  costs,  and  not  as  annual  expenses,  when 
reckoned  in  cost  accounts  for  the  stand.     In  a  forest  under 
perfect  management,  costs  of  most  of  these  operations  consti- 
tute a  nearly  constant  annual  expense  for  the  forest  as  a  whole, 
and  would  so  appear  in  the  proprietary  account. 

100.  Protection  Expenses.  —  Initial  expenses  for  protection 
from  fire  take  the  form  of  measures  for  disposal  of  slash  left  from 
logging.     This  expense  is  chargeable  to  the  cost  of  the  new 
crop  and  may  be  so  treated  in  a  cost  account.     But  in  practice, 
where  the  owner  is  not  doing  his  own  logging,  as  in  the  United 


INVESTMENTS  AND  COSTS  IN  FOREST  PRODUCTION         75 

States  Forest  Service  operations,  this  cost  is  transferred  wholly 
or  in  part  to  the  logger,  and  taken  out  of  the  price  of  stumpage. 
By  this  means,  the  true  nature  of  the  expense  is  concealed. 
The  loss  in  stumpage  value  is  a  present  cost  or  investment  in  the 
new  crop  as  surely  as  if  the  owner  received  full  value  for  the  tim- 
ber and  re-expended  the  amount  required  for  brush  burning. 
This  initial  cost,  then,  accumulates  interest  until  the  new  crop 
is  cut  (§  107).  For  this  reason,  it  has  been  advocated  as  an 
alternative,  that  a  sum  representing  merely  the  annual  interest 
on  this  initial  expense  could  be  expended  annually  on  the  area 
to  secure  better  protection  from  fire,  without  increasing  the 
total  outlay. 

Fire  lines  will  frequently  be  necessary,  particularly  where  a 
bad  hazard  occurs  and  where  an  investment  has  been  made  in 
plantations.  This  constitutes  a  capital  expenditure,  especially 
where  the  initial  cost  of  the  lines  greatly  exceeds  their  subse- 
quent cost  of  maintenance.  The  charge  must  be  pro-rated 
over  the  area  benefited,  dated  from  the  year  it  was  incurred. 
Subsequent  maintenance  of  these  lines,  a  necessity  often  lost 
sight  of,  is  an  annual  charge  per  acre. 

Lookout  towers  and  installation  of  telephones  used  in  fire 
protection  are  of  the  same  class  of  expenditure  as  fire  lines. 

The  labor  employed  in  fire  protection  for  patrol  constitutes 
an  annual  charge. 

Extra  costs  of  extinguishing  fire,  if  borne  by  the  owners,  con- 
stitute losses,  entered  against  the  area  burned,  and  recoverable 
in  some  cases  as  damages. 

101.  Administrative  Expenses.  —  With  a  large  area  and 
well-developed  system  of  forest  production,  the  administration 
of  the  tract  involves  not  only  all  business  matters  dealing  with 
sale  of  products,  taxes,  protection  and  silviculture,  but  includes 
as  well  the  proper  technical  direction  of  the  work  to  assure 
the  success  of  the  measures  for  forest  production  which  are 
the  basis  of  the  business.  The  salary  of  a  technical  forester  is, 
therefore,  a  necessity,  and  this  must  be  pro-rated  on  an  area 
basis.  Should  the  tract  be  too  small  to  justify  such  expense, 
the  owner  must  seek  occasional  technical  advice  and  trust  the 


76  FOREST  VALUATION 

management  to  a  foreman  who  can  follow  directions.  Such 
advice  is  best  obtained,  for  very  small  areas,  through  the  State 
forester.  For  larger  areas  it  is  practicable  for  several  owners 
to  co-operate  and  employ  a  forester. 

102.  Taxes  and  Insurance.  —  Taxes  are  separately  discussed 
in  Chapter  X.     Under  present  systems  of  taxation  they  tend  to 
increase  and  this,  coupled  with  the  uncertainty  as  to  the  amount 
and  time  of  these  increases,  makes  it  difficult  to  predict  the  total 
cost  of  this  item  or  prescribe  the  exact  method  of  calculating 
it.     In  this  chapter,  taxes  will  be  assumed  as  a  fixed  annual 
expense,  to  be  added  to  that  for  administration  and  protection. 

Insurance  is  not  as  yet  available  in  this  country  on  growing  or 
standing  timber.     The  owner  bears  his  own  risk  and  losses. 

103.  Interest  Charges.  —  These  do  not  appear  in  proprietary 
accounts  except  when  money  is  borrowed  (§91).     In  cost  ac- 
counts, past  interest  may  at  any  time  be  calculated  at  whatever 
rate  is  considered  equitable.     Since  the  periods  intervening  be- 
tween outlay  and  income  may  extend  to  over  100  years,  the 
interest  charges  will  often  be  found  to  far  exceed  the  sum  of  all 
actual  expenditures. 

104.  Classification  of  Costs  in  Forest  Production.  —  Follow- 
ing the  suggestions  in  the  above  analysis  of  costs,  the  invest- 
ments in  forest  production  may  be  grouped,  for  computation, 
into  three  classes: 

Group  A . 

Capital  expenditures  for 

Land. 

Permanent  improvements  and  equipment. 

Permanent  roads  and  firelines. 
Group  B. 

Crop  expenses  for 

Standing  timber,  which  is  often  included  with  cost  of  land. 

Planting  or  cost  of  regeneration. 

Brush  disposal  or  initial  fire  protection. 

Weeding. 

Protective  operations. 

Thinning. 


INVESTMENTS  AND  COSTS  IN  FOREST  PRODUCTION         77 

Group  C. 

Annual  or  current  expenses  for 
Protection. 
Administration. 
Taxes. 
Maintenance  of  permanent  improvements. 

105.  Calculation  of  Total  or  Final  Costs.  —  To  compute  the 
total  final  cost,  with  interest  included,  at  the  end  of  a  given 
period,  the  items  under  each  of  these  three  classes  may  be 
totalled. 

The  "cost"  of  each  is  the  amount  which  should  be  charged 
against  the  resulting  income,  which  in  forestry  is  the  stumpage 
value  of  the  timber  plus  the  revenue  from  other  sources. 

In  Group]  A,  the  original  capital,  if  maintained  properly,  re- 
mains intact  at  the  end,  and  only  the  interest  can  be  charged  as 
an  expense  to  the  crop.  Let  Sc  =  cost  of  soil  and  permanent 
improvements.  Then  total  cost  is 

Se  (!.<#")-£.  (§87,  Illb) 

In  Group  B,  only  those  crop  expenses  which  occur  in  the  same 
year  may  be  computed  as  one  total.  These  expenses  must 
eventually  be  met  entirely  from  income  and  do  not  constitute 
capital  expenditures.  With  the  cutting  of  the  timber,  no  por- 
tion of  the  remaining  assets  are  available  from  which  to  return 
these  costs. 

The  total  cost  of  all  such  items  is  found  by  Formula  I  in  which 
C  =  initial  investment, 
C  (i.opn)  =  cost  at  end  of  period. 

Expenses  incurred  in  year  d  will  cost 

Q(i.o^-<0. 

Let  C0,  Cd,  Ce,  Cf  =  Initial  expenses  incurred  in  the  beginning 
and  in  the  years  d,  e  and  /.  The  sum  of  these  costs  is 

C0  (i.ctf»)  +  Cd  (i.op»~d)  +  Ce  (i.op»-e)  +  C,  (i.o^-O- 
In  Group  C,  all  annual  expenses  are  totalled.    The  sum  of  this 
expense  with  interest  is  found  by  Formula  Illb  (§  87). 
Substitute  e  for  r  to  represent  annual  expense. 


78  FOREST  VALUATION 

Then  — —  =  R  =  E.  capitalized  annual  expense. 

o.op 

The  sum  of  these  expenses,  provided  they  remain  at  a  constant 
annual  amount,  is 

E  (i.o/>B)  -  E  =  E  (i.opn  -  i). 

The  analogy  of  this  calculation  to  that  used  in  Group  A  is 
evident.  The  difference  is  that  in  A,  Se  represents  existing 
capital  which  remains  as  an  asset,  while  in  C,  E  represents 
a  fictitious  capital  which  may  have  no  existence  and  is  never 
expended.  It  represents  the  capital  which  would  be  tied  up, 
in  order  to  produce  an  income  to  just  balance  the  expense  e. 
This  capital  might,  if  the  owner  desired,  be  actually  deposited 
at  interest,  when  the  expense  e  would  be  permanently  taken 
care  of  and  the  capital  remain  intact  at  the  end  as  in  Group  A. 
But  the  proprietor  usually  meets  this  expense  out  of  income 
from  other  sources.  The  capital  represented  by  E  is,  therefore, 

merely  a  mathematical  device,  and  the  expression better 

o.op 

expresses  the  status  of  the  item,  as  it  emphasizes  the  annual 
expense. 
Should  expenses  increase,  the  modified  Formula  Ilia  is  used, 

by  substituting  E'  for  -^-  (§  79) . 
o.op 

The  total  actual  cost  of  production  for  timber  grown  under 
management  covers  the  period  from  its  origin  to  its  removal. 
Adding  the  summaries  for  the  three  groups,  we  have 

Gc  =  C  (i.opn)  +  Sc  (i.opn  -  i)  +  E  (i.opn  -  i) 

=  (C  +  Sc  +  E)  i.opn  -  (Sc  +  E).  (A) 

This  formula  suffices  when  all  initial  crop  expenses  occur  in 
the  first  year. 

Income  during  this  period  serves  to  cancel  an  equal  value  of 
accumulated  costs  in  the  year  in  which  it  is  received.  Annual 
income  usually  serves  merely  to  reduce  the  net  annual  cost,  and, 
therefore,  does  not  appear  in  the  formula.  But  income  received 
from  the  sale  of  produc.ts  obtained  from  advance  cutting,  or 
thinnings,  bears  no  constant  relation  to  the  total  expenses  for 


INVESTMENTS  AND   COSTS  IN  FOREST  PRODUCTION         79 

the  year.  All  income  is  equivalent  to  negative  costs,  and  in 
this  case  the  item  is  best  carried  with  interest  to  the  final 
year,  when  its  total  may  be  subtracted  (§  77).  Otherwise  a 
separate  balance  would  be  required  for  the  year  of  receipt  of 
this  income,  which  would  serve  no  useful  purpose. 

Let  Tp,  Tq,  Tr  =  value  of  thinnings  or  other  incidental  rev- 
enue received  at  p,  q  and  r  years.  The  future  value,  at  end  of 
period,  will  be 

Tp  (i.op*->)  +  Tq  (i. <#--«)  +  Tr  (i.op"-'). 

Subtracting  this  income  from  total  cost,  including  Cd,  Ce  and 
Cf,  we  have  the  net  cost  of  the  growing  stock,  Gc. 
Gc  =  (C  +  SC  +  E)  i.opn  +  Cd  (i.opn~d) 

+  Ce  (i.o/>"-«)  +  Cf  (i.o^-O  -  Tp  (i.op"->) 

-  Tq  (i. <#"-«)  -  Tr  (i.o^-")  -  (Se  +  E).          (AO 

There  is  no  way  of  avoiding  these  separate  calculations  for 
single  sums  occurring  in  odd  years.  As  each  item  is  independent 
of  the  others,  the  apparent  complexity  of  these  formulae  need 
not  be  a  source  of  confusion. 

To  obtain  the  cost  of  a  forest,  including  both  soil  and  timber, 
the  cost  of  soil  is  not  subtracted. 
Let  Fc  =  cost  of  forest. 

Then  Fc  =  (C  +  Sc  +  £)  i.op*  -  E, 

and  for  the  year  a, 

°FC  =  (C  +  Sc  +  E)  i.op*  -  E.  (A2) 

106.  Total  Cost  of  Investments  in  Standing  Timber.  —  Only 
a  few  instances  are  found  in  America  where  forest  crops  have 
been  brought  from  seed  to  maturity  under  management,  and 
it  is  still  less  frequently  that  actual  total  costs  of  production 
have  been  recorded.  Practically  all  past  transactions  in  land, 
for  forest  purposes,  dealt  with  property  which  already  contained 
standing  timber. 

Cost  accounts  for  such  property  begin  with  the  purchase  price 
and  carry  all  subsequent  net  expenses  to  the  present,  to  final 
sale  of  the  property,  or  to  the  year  when  the  timber  is  sold. 
Since  such  property  is  purchased  in  a  partially  or  fully  developed 


80  FOREST  VALUATION 

condition,  with  respect  to  the  timber  crop,  and  may  include  cer- 
tain permanent  improvements,  the  cost  to  the  purchaser  may  not 
coincide  with  the  cost  of  production,  for  the  sale  is  usually  the 
means  of  realizing  profit  on  the  part  of  the  original  owner  (§  90). 
This  initial  cost  is  usually  a  lump  sum,  which  includes  the  value 
not  only  of  all  separate  stands  of  timber,  but  does  not  often 
separate  the  value  of  the  land  from  that  of  the  timber  crop.  An 
analysis  of  this  cost  must  precede  any  attempt  to  institute  a 
cost-keeping  system  separately  for  different  parcels  or  stands. 

Separation  of  the  cost  of  land  and  timber,  while  usually 
postponed  in  such  instances  until  actual  separation  occurs 
through  cutting,  is  necessary  if  the  true  cost  of  holding  the  timber 
is  to  be  computed,  and  the  land  permanently  devoted  to  for- 
estry. But  if  the  purchase  is  a  timber  speculation,  and  the 
land,  after  the  timber  is  stripped  from  it,  is  to  be  sold  or  aban- 
doned, there  will  be  no  need  of  this  distinction. 

In  the  former  case, 

C+SC  =  cost  of  timber  and  land,  or  purchase  price  of  property. 

The  purchase  price  of  the  property  is  substituted  for  cost  of 
land  plus  silvicultural  operations,  in  Formula  A.  The  net  cost 
of  production  for  timber  depends  now  upon  the  value  agreed 
upon  for  the  land  at  time  of  purchase,  for  this  must  be  subtracted 
as  representing  a  capital  investment.  The  formula  is  in  all  re- 
spects identical  with  A,  and  interest  accumulates  for  the  period 
elapsing  between  date  of  purchase  and  date  of  final  sale  or  in- 
come, which  is  assumed  as  n  in  the  problem. 

When  interest  is  thus  computed  as  a  cost  on  the  investment 
in  stumpage,  as  well  as  on  taxes  and  other  expenses,  a  rate  of 
6  per  cent  will  cause  this  "cost"  to  double  in  twelve  years. 
The  stumpage  value  must  double  in  a  shorter  period  or  there 
will  be  no  income  to  replace  current  expenses.  This  raises  the 
important  question  as  to  the  length  of  time  which  it  is  possible 
for  private  owners  to  hold  stumpage  without  cutting  it  (§  181). 
For  periods  of  forty  years  or  over,  it  might  easily  be  shown  that 
the  costs  of  raising  a  new  crop  of  timber  leave  a  higher  margin 
of  profit  than  those  incurred  in  carrying  a  mature  crop  with  a 
high  initial  value,  for  the  same  length  of  time. 


INVESTMENTS  AND   COSTS  IN  FOREST  PRODUCTION         8l 

107.  Costs  of  Forestry  Compared  with  Destructive  Lum- 
bering. —  Owners  of  timberlands  have  the  choice  of  two  lines 
of  policy.  They  may  desire  to  retain  the  lands  only  until  the 
timber  is  removed,  when  every  effort  will  be  made  to  sell  or 
dispose  of  them.  Or  they  may  plan  to  hold  these  lands  indefi- 
nitely, with  the  intention  of  producing  or  securing  a  new  growth 
of  trees.  The  former  policy  is  usually  accompanied  by  destruc- 
tive lumbering,  so  termed  because  the  purpose  of  the  operation 
is  to  remove  every  tree  of  merchantable  value,  at  the  same  time 
undertaking  no  measures  to  reproduce  or  perpetuate  the  forest. 

The  financial  distinction  between  these  two  policies  lies  in 
the  character  of  the  investment  required  for  forestry.  Destruc- 
tive lumbering  squeezes  the  last  cent  of  capital  from  the  forest, 
wrecking  it  as  a  productive  enterprise,  and  converting  it  into 
money  profits.  In  this  process,  the  cost  of  transportation  is 
reduced  to  a  minimum  by  use  of  temporary  structures  and  com- 
plete removal  of  the  timber,  by  elimination  of  all  care  in  felling 
and  skidding  needed  in  preventing  injury  to  young  timber,  and 
by  neglect  of  the  fire  trap  caused  by  the  slash,  and  abandonment 
of  the  land  to  promiscuous  broadcast  burning.  Under  such 
conditions,  stumpage  brings  its  highest  prices  and  the  profits  to 
logger  and  owner  are  greatest  in  amount.  But  there  they  cease. 

In  any  other  form  of  business,  similar  results  may  be  obtained 
should  the  owner  close  out  the  enterprise  by  the  sale,  not  only 
of  the  net  product,  but  of  his  reserve  stock,  fixtures  and  capital 
assets.  The  profits  obtained  on  stumpage  under  destructive 
lumbering  are  higher  than  the  business  of  forest  production 
can  earn  or  is  entitled  to,  and  the  entire  structure  of  lumbering 
as  it  is  carried  on  to-day  will  crumble  away  with  the  exhaustion 
of  the  raw  materials,  having  converted  the  chief  asset,  produc- 
tiveness of  forest  lands,  into  money. 

The  investment  which  forestry  may  require,  and  which  de- 
structive lumbering  avoids,  consists  of 

Additional  cost  of  transportation  in  logging. 

Additional  felling  and  skidding  costs. 

Brush  disposal. 

Cost  of  seed  trees. 


82  FOREST  VALUATION 

With  the  entire  cost  of  building  roads  charged  against  the 
logging,  and  pro-rated  over  the  amount  of  timber  logged,  any 
reduction  in  this  quantity,  especially  if  the  area  is  not  corre- 
spondingly reduced,  increases  the  unit  cost  of  logging  by  nearly 
the  same  ratio.  It  is  not  often  possible  to  cheapen  the  means 
of  transportation  to  conform  to  the  lessened  cut  (§  98). 

Felling  and  skidding  will  cost  more  in  proportion  to  the  care 
needed  in  avoiding  damage  to  young  timber. 

Brush  disposal  (§  100)  is  almost  always  needed.  It  frequently 
happens  that  as  a  result  of  this  measure,  the  costs  of  skidding 
are  correspondingly  reduced. 

A  question  may  well  be  raised  as  to  whether  the  sum  of  these 
extra  expenses  constitutes  a  loss  of  profits  on  the  crop  being  cut 
or  a  diversion  of  profits  into  initial  investments  on  the  next 
crop.  Should  the  total  extra  cost,  thus  incurred,  be  charged  as 
initial  cost  or  silvicultural  expenses,  to  accumulate  at  compound 
interest,  it  would  constitute  a  heavy  burden  on  the  succeeding 
crop.  Viewed  from  the  standpoint  of  destructive  lumbering, 
this  cost  taken  from  profits,  is  a  deliberate  reduction  of  ordinary 
profits  and  must  be  charged  against  future  income.  But  from 
the  standpoint  of  forest  production,  this  excess  profit  is  not  a 
true  profit  at  all,  but  the  wrecking  value  of  the  "plant"  added 
to  legitimate  profit.  Normal  profit  is  that  which  will  leave  the 
productive  capital  intact.  From  this  standpoint  these  "extra" 
costs  of  logging  would  be  considered  as  "ordinary"  costs,  falling 
on  the  logging  and  cancelled  by  income  from  sale  of  logs,  and 
would  not  be  regarded  as  an  additional  investment  in  the  new 
crop.  These  two  opposing  tendencies  are  best  illustrated  by 
the  expense  of  burning  brush  (§  100). 

The  investment  represented  by  the  stand  of  timber  left  after 
logging  is  more  easily  classified.  Should  this  consist  merely  of 
seed  trees,  it  can  be  regarded  as  a  loss  only  in  case  these  trees 
will  not  live  until  the  harvesting  of  the  next  crop.  If  they 
survive,  they  represent  an  investment  from  which  the  returns 
will  be: 

The  future  value  of  the  trees  themselves; 

The  value  of  the  new  crop. 


INVESTMENTS  AND   COSTS  IN  FOREST  PRODUCTION         83 

This  investment  feature  is  even  more  conspicuous  in  the  case 
of  stands  in  which  a  large  per  cent  remains  after  logging. 

In  either  case,  the  sale  of  the  greater  portion  of  the  merchant- 
able stand  gives  the  basis  for  an  appraisal  of  the  remaining  timber. 
A  balance  may  be  struck  between  past  costs  and  income  and 
the  remaining  crop  credited  with  its  present  value,  which  is 
then  charged  as  an  initial  investment  for  the  ensuing  period. 
This  would  show  profits  on  the  entire  crop,  and  a  reinvestment 
of  the  portion  left  standing.  If  this  appraisal  is  not  used,  the 
profits  are  confined  to  the  timber  actually  cut,  and  the  invest- 
ment would  not  be  charged  against  the  new  crop  or  period. 

The  former  method  of  accounting  is  preferable.  The  use  of 
profits  to  cancel  investment  may  be  pushed  to  illegitimate 
lengths,  as  when  income  from  the  sale  of  timber  is  allowed  to 
"  wipe  out"  the  cost  of  the  land,  which  is  then  carried  as  having 
no  "cost"  or  "value"  for  a  succeeding  period.  In  this  case, 
income  from  sales  should  be  permitted  to  offset  only  the  cost 
of  the  timber  sold,  while  the  land  (§  96)  must  be  separately 
valued,  and  will  be  charged  with  interest  in  the  future  reckoning. 

108.  Cost  of  Many-aged  Forests.  —  Proprietary  accounts  of 
investment  for  large  forest  properties  are  kept  very  simply  (§91). 
The  same  is  true  of  such  an  account  when  dealing  with  single 
stands  composed  of  trees  of  many  ages.  But  the  question 
arises  as  to  whether  income  from  such  a  stand  should  cancel 
original  capital  investments,  or  be  regarded  purely  as  interest 
or  dividends  on  this  capital. 

If  the  forest  is  established  and  is  renewed,  so  that,  whether 
the  cutting  be  annual  or  at  intermittent  periods,  it  may  be 
maintained  in  amount  and  value  indefinitely,  the  cost  of  the 
stand  can  be  considered  as  a  unit,  regardless  of  the  separate 
age  classes  (§  161).  This  cost  may  be  the  price  of  purchase  or 
the  cost  of  production  (§  109).  In  a  stand  of  all  ages,  producing 
annual  income,  this  cost  does  not  increase  and  the  net  income  is 
merely  the  annual  dividends  on  the  investment.  None  of  this 
income  is  needed  for  the  replacement  of  capital. 

In  a  forest  yielding  an  intermittent  rental,  the  cost  or  total 
investment  continues  to  increase  (§  92)  until  a  payment  of 


84  FOREST  VALUATION 

income  is  received.  This  payment  must  be  regarded  as  can- 
celling the  additional  capital  invested  since  the  last  payment. 

Where  yields  are  irregular  in  time  and  value,  and  yet  there 
always  remains  a  considerable  stand  of  timber  on  the  ground, 
the  relation  between  cost  and  income  becomes  a  matter  of  judg- 
ment or  adjustment.  The  object  should  be  to  insure  the  return 
of  the  capital  invested  in  the  timber  which  is  removed,  and  carry 
as  a  cost  or  further  investment  only  a  reasonable  balance  of 
original  cost  against  future  income.  The  cost  of  a  forest  is  the 
sum  of  the  net  costs  of  the  separate  stands  or  parcels. 

109.  Cost  of  Producing  a  Normal  Forest.  —  A  normal  forest 
is  one  from  which  an  annual  income  may  be  obtained  without 
diminishing  the  amount  and  value  of  the  capital  or  assets.  This 
requires  the  presence  of  equal  productive  areas  in  each  age  class. 

Granting  that  the  cost  of  each  parcel  of  land  is  charged  to 
this  forest  in  the  year  in  which  the  crop  upon  it  is  started,  and 
that  it  takes  n  years  to  establish  the  forest,  an  area  equal  to 

-  of  the  whole  must  be  reproduced  each  year.  The  total  annual 
n 

expense  e  applies  to  the  entire  area  of  the  forest.  C  is  required 
to  plant  the  parcel.  The  capital  tied  up  in  the  investment 
for  the  year  will  then  be  C  +  Sc  +  E  (§  105). 

Since  an  equal  area  and  capital  investment  is  added  each  year, 
on  which  interest  accumulates  till  the  year  n,  the  sum  of  costs 
forms  a  series,  with  (C  +  Sc  +  E)  as  the  first  term  and  i.op 
as  the  ratio  of  increase.  See  Formula  III. 

The  sum  of  these  costs  is 


o.op 

But  the  capital  E  is  fictitious  (§  104)  and  this  has  been  intro- 
duced n  times.  In  the  same  way,  Se  may  be  deducted  as  a 
capital  asset,  totalling  nSc. 

This  makes  the  net  cost  of  production  for  the  timber  alone  as 


(A,) 


CHAPTER   VII 
THE   VALUATION   OF   FORESTS 

110.  Valuation  Accounts  in  Forestry.  —  Just  as  the  proprie- 
tary and  cost  accounts  in  forestry  (Chapter  VI)  deal  with  the 
personal  investments  of  the  owner  and  past  elements  of  cost 
and  income,  so  the  valuation  accounts  in  forestry  deal  entirely 
with  material  assets  (§  54)  and  determine  their  value.      The 
basis  of  this  determination  is  the  forest  inventory  (§  55)  which 
shows  the  area  of  land  of  different  qualities,  the  amount  and 
kind  of  timber  and  of  other  resources,  and  any  other  property 
included  in  the  forest. 

111.  Income  as  the  Basis  of  Value  of  Forests.  —  This  phys- 
ical property  must  be  valued  or  appraised  (§§  18,  60).     Follow- 
ing the  conservative  systems  of  accountants,  the  values  entered 
for  land,  timber,  buildings  or  other  forms  of  property  cannot 
exceed  what  was  actually  paid  for  them  (§56).     Such  an  asser- 
tion does  not  mean  that  the  actual  value  of  the  property  remains 
at  cost,  but  that  growth  in  value  is  not  considered  equivalent 
to  realized  income.     An  increase  in  value  of  assets  may  and 
does  occur,  and,  with  growing  timber,  is  the  rule;  but  the  ac- 
countant in  all  such  cases  desires  to  await  the  actual  sale  of  the 
product,  and  credits  this  increase  in  value  only  when  received 
in  the  form  of  money  returns. 

While  this  custom  protects  the  proprietor  or  stockholder,  no 
pretense  is  made  that  the  book  values,  based  on  cost,  represent 
the  actual  value  of  the  property.  In  Chapter  IV  the  basis  of 
value  is  seen  to  be  future  income  (§§  61  and  62)  and  the  true 
value  of  all  assets  is  derived  from  this  income,  discounted  to 
the  present,  minus  future  costs. 

In  order  to  grasp  the  principles  employed  in  appraising  for- 
est values,  the  relations  between  physical  assets,  income  and 
value  must  again  be  emphasized.  First,  the  forest  land,  with 

85 


86  FOREST  VALUATION 

its  growth  or  stand  of  timber,  is  the  property  to  be  valued. 
Second,  this  land,  by  producing  timber,  and  the  timber,  by  grow- 
ing, yields  saleable  products  whose  final  sale  produces  income. 
Third,  the  income,  expressed  in  money,  has  an  appraised  value. 
As  the  final  step,  the  value  of  the  income  is  discounted  to  deter- 
mine the  value  of  the  physical  capital  which  will  produce  it. 

This  process  cannot  be  short-circuited.  The  sale  value  of 
forest  land  or  timber  does  not  represent  any  quality  inherent 
in  the  land  or  timber  except  the  capacity  to  produce  income, 
and  the  value  of  the  property  must  first  be  based  on  the  valua- 
tion of  the  income. 

The  income  from  forests  is  principally  the  value  of  timber 
sold  on  the  stump,  or  the  proportion  of  profits  from  logging 
which  is  due  to  the  owner  of  stumpage.  Secondary  income  is 
obtained  from  thinnings  or  advance  cuttings,  and  from  pastur- 
age, or  hunting  and  fishing  rights.  Other  sources  of  income  are 
by-products,  such  as  naval  stores,  or  tree  seeds,  nuts,  bark, 
sugar,  shrubs,  herbs  and  litter. 

The  present  value  of  the  forest  is  the  sum  of  the  present  or 
discounted  values  of  all  items  of  income  expected  in  the  future, 
less  the  present  value  of  all  items  of  anticipated  expense  (§  62). 

Sale  value  bears  the  same  relation  to  capital  or  expectation 
value  for  forests  as  for  any  other  form  of  property  (§  59).  But 
since  sale  values  are  the  expression  of  average  general  opinion, 
the  sale  value  of  forest  land  and  young  timber  will  be  apt  to 
depart  widely  from  the  capital  or  expectation  value  of  such 
property  in  regions  where  the  business  of  forest  production  is 
not  recognized,  and  lands  are  abandoned  after  logging  or  de- 
voted to  agriculture  and  grazing. 

112.  Value  of  Forest  Property  for  Destructive  Lumbering.  — 
When  the  owner  intends  to  remove  the  timber  and  devote  the 
land  to  other  uses,  his  income  will  consist  of: 

Yield  of  timber; 

Value  of  land  for  other  purposes  after  timber  is  removed. 

As  long  as  the  timber  remains,  the  land  cannot  be  utilized 
fully  for  anything  but  the  timber  crop.  Grazing  is  only  a  sec- 
ondary source  of  revenue.  When  cleared,  its  value  is  considered 


THE  VALUATION  OF  FORESTS  87 

as  depending  solely  on  the  net  future  income  from  other  uses, 
such  as  agriculture  or  grazing.  Since  these  are  enterprises  not 
directly  connected  with  forestry,  it  may  be  technically  assumed 
that  the  forest  owner  sells  the  land,  and  the  sale  value  received 
completes  his  income  and  terminates  the  enterprise. 

The  total  present  value  of  forest  property  based  on  the 
income  from  destructive  lumbering  is  determined  as  follows: 

Fa  =  sale  value  of  forest  property,  including  both  land  and 

timber: 

Y  =  yield  or  net  stumpage  value  of  timber  in  final  cutting. 
Tp,  Tq)  Tr  =  yield  or  value  of  thinnings  or  timber  removed 

before  final  cutting. 

Ss  =  sale  value  of  land  when  finally  cleared  of  standing  timber. 
e  =  annual  expenses. 
E  =  capital  value  of  annual  expenses. 
a  =  present  year,  or  the  year  a  dating  from  the  origin  of  the 

stand. 
n  =  year  in  which  final  cutting  is  made,  dating  from  the  origin 

of  the  stand. 

The  period  of  discount  will  then  be  n  —  a  years. 

In  the  year  of  sale,  and  previous  to  its  consummation,  a  and 
n  coincide.  The  value  of  the  property  for  immediate  sale  is 
then 

F.  =  Y  +  S..  (B) 

When  the  year  of  valuation  a  precedes  n,  the  value  is  as 
follows  : 

Value  of  Y  for  year  a 


Value  of  Tp,  Tq,  Tr  for  year  a 


Value  of  Sg  for  year  a 

Ss 


88  FOREST  VALUATION 

Cost  of  e  for  n  -  a  years  =  E  (l'°p™~  ^  (see  Illb,  II),  which 
becomes  E 


i.opn  ° 
Omitting  the  item  of  thinnings, 


Y+Ss-E(i.opn-°- 
r  .  =  — 

i.opn  a 


. 

i.opn  a 

Including  thinnings  whose  income  is  expected  in  the  future,  or 
between  the  years  a  and  n, 


(B2) 

113.  Value  of  Forest  Property  for  Continuous  Forest  Pro- 
duction. —  The  substitution  of  sale  value  of  land  for  its  value 
determined  from  income  was  a  makeshift  justified  by  the 
change  in  its  use.  True  forest  land,  devoted  permanently  to 
producing  timber,  must  be  valued  on  the  basis  of  the  sum  of  all 
future  income  which  it  is  capable  of  producing.  This  will  in- 
clude the  net  value,  not  merely  of  the  present  stand,  but  of  a 
succession  of  timber  crops,  extending  to  infinity  (§  86). 

The  relative  present  value  of  the  first  crop  compared  with 
others  to  follow  is  very  large,  but  merely  because  the  interval 
between  payments  is  correspondingly  long.  The  income  from 
sale  of  a  crop  of  timber  does  not  differ  in  character  from  the 
monthly  payment  of  rent,  and  the  value  of  the  forest  is  as  truly 
the  sum  of  all  present  values  from  future  crops  as  that  of  the 
house  is  the  capitalized  net  rental  or  income.  In  the  same  way 
that  the  value  of  the  house  represents,  not  the  gross  rent,  but 
the  rent  minus  all  outlay  such  as  taxes,  repairs  and  depreciation, 
so  from  all  future  income  from  timber,  deductions  for  expenses 
must  be  made  to  get  total  net  value. 


THE  VALUATION  OF  FORESTS  89 

114.  Value  of  a  Forest  of  Even  Age  Just  Previous  to  Cutting. — 
A  forest  or  stand  of  even  age  may  be  cut  clear  at  one  time  and 
replanted.  During  the  period  immediately  following  the  cut- 
ting, the  soil  is  bare  of  trees,  while  at  all  other  times  it  is  occupied 
by  timber  of  constantly  increasing  size. 

Since  every  item  of  either  income  or  expense  must  be  assumed 
to  recur  for  each  future  timber  crop,  the  total  present  or  dis- 
counted value  for  each  item  is  found  by  Formulae  IX  to  XII. 

For  the  year  n,  and  just  previous  to  receipt  of  income  Y,  the 
value  of  income  Y,  being  the  sum  of  all  future  payments  dis- 
counted to  the  present  year,  is 


The  cost  of  planting  or  reproduction,  which  in  destructive 
lumbering  does  not  occur,  falls  here  in  the  same  year  as  F  and 
recurs  every  n  years. 

Value  of  expense  C,  totalled  in  the  same  manner,  is 

c  +  ^_+    c    +...+^_  =  c  +  _^. 

I. Op  I. Op*  I. Op  I. Op    —  I 

The  annual  expenses  e  recur  at  intervals  of  i  year,  by  defini- 
tion, and  are  computed  from  the  end  of  each  year. 
Value  of  the  sum  of  annual  expenses  e: 

e  e  e  e  e  e     _  „ 

i. op      i.opz      i. op3  i.opx       i. op—  i      o.op 

Let  Fv  =  expectation  or  capital  value  of  forest  property  for 
continuous  production. 
Then 


which  is  the  value  of  forest  property  just  previous  to  removal 
of  the  timber. 

In  this  formula,  no  account  has  been  taken  of  other  items  of 


90  FOREST  VALUATION 

expense  corresponding  to  C  but  falling  at  different  years,  nor 
of  income  from  thinnings  corresponding  to  Y  but  received 
previous  to  this  final  cut. 

The  present  value  of  these  items  is  found  by  Formula  X,  since 
each  single  payment,  while  not  repeated  during  the  rotation,  is 
assumed  to  recur  in  the  next  rotation,  and  the  total  of  all  future 
payments  forms  the  series. 

Let  TP  =  income  from  thinning  in  year  p,  recurring  every  n 
years  forever. 

T 

Then  — —  is  the  value  of  TP  in  the  first  year,  n. 


i.op 


By  substituting  q,  or  r,  for  p,  the  present  capital  value  of 
other  items  of  income  or  of  expense,  for  any  year,  is  obtained. 

The  present  value  of  forest  property  just  previous  to  removal 
of  a  final  cut  of  timber  is  summed  up  as 


Tr  (l.O^-O    ~C-Cd 


F  =Y      (C  |  £)   | 

i.opn—  i 

115.  Value  of  an  Even-aged  Forest  for  Any  Year.  —  The  value 
of  the  forest  for  any  other  year,  or  during  its  growth,  is  ob- 
tained by  discounting  the  above  value  for  the  period  previous 
to  this  final  cut.  The  forest  has  its  maximum  value  just  before 
the  principal  yield  is  removed.  The  further  into  the  future  this 
income  is  postponed,  the  less  becomes  the  present  value  of  the 
property. 


THE  VALUATION  OF  FORESTS  91 

Should  the  value  be  sought  for  the  year  a,  and  this  year  be 
but  one  year  previous  to  the  cut,  the  value  of  the  forest  is  dis- 
counted n  —  a,  or  one,  year.  As  a  is  dated  earlier  and  earlier 
in  the  life  of  the  stand,  the  discount  period  n—  a  increases,  until 
when  a  =  o,  just  after  the  f elling  of  the  old  crop  and  previous  to 
the  starting  of  the  new  one,  we  get  the  smallest  value  to  which 
the  property  shrinks  in  the  entire  rotation. 

With  the  advance  of  the  date  of  calculation  to  the  year  a, 
both  the  future  yield  7  and  the  cost  of  planting  C  occur  first 
in  n  —  a  years.  The  annual  expenses,  since  they  are  calculated 
for  the  same  interval,  and  extend  to  infinity  in  both  cases,  have 
the  same  capital  value  E. 

By  Formula  Xa,  the  value  of  the  forest  is 


(D) 


Items  of  either  income  or  expense  occurring  at  other  than  n 
years  will  fall  either  previous  to  or  subsequent  to  year  a.  Those 
preceding  a  are  not  considered  in  the  value  of  the  standing  crop 
(§68),  but  their  occurrence  in  the  subsequent  rotations  affects 
the  value  of  the  forest. 

A  thinning  occurring  in  the  year  r  subsequent  to  a  has  a  value 

T 

at  present  (year  a)  of  —     — 
r~° 


The  sum  of  future  values  (Q4)  is 
Tr 


j. I.0pn  - 


i.opn 

A  thinning  occurring  in  the  year  p  previous  to  a^  has  a  present 

value  (year  a)  of  ^ 

u         '       i.opp+n~a 


92  FOREST  VALUATION 

The  sum  of  future  values  (Q4)  is 
Tp 


i.opn—  i 


These  expressions  are  equally  applicable  to  costs  occurring 
before  or  after  the  year  a.  The  present  value,  in  year  a,  of  an 
even-aged  forest  or  stand,  is  summed  up  as 

Y  (i.opa)  +  Tp  (i.op*-p)  +  Tq  (i.opa-«) 
+  Tr  (i.op-+°-r)  -  C  (i.o^)  -  Cd  (i. 


i.opn—  i 
This  formula  may  be  expressed  in  another  form. 

+ i.n  + j,r  ^   ~'. 


-  E. 


_  ___ 

i.opp     i.opq         i.opr  i.o/>d     i. op*     i.op'J  '  *    _E 

i.opn-i 

(Di) 

The  chronological  relations  of  these  items  are  set  forth  in 
Diagram  II.  The  present  year  is  the  basis  of  valuation.  Past 
occurrences  are  ignored.  But  in  the  terminology,  the  numerical 
value  of  a  is  reckoned  from  the  past  year  o,  or  date  of  origin 
of  the  crop,  which  is  also  the  basis  for  the  other  dates. 

The  year  20  is  just  n  years  in  the  future.  The  Formula  DI 
expresses  the  value  of  the  items  computed  at  compound  interest 
to  the  year  20.,  when  the  balance  is  struck  which  gives  net 
value.  This  net  income  recurs  at  intervals  of  n  years  from 

date,  and  its  present  value  is  —         — ,  hence  the  above  result. 
i.opn  —  i 

116.  Value  of  Forest  Soil.  —  The  value  given  in  Formula  C 
was  for  a  forest  just  previous  to  removal  of  the  final  cut.  This 
value  steadily  diminishes  as  the  date  of  this  cut  is  assumed  to 
be  further  into  the  future  until  the  lowest  ebb  is  reached,  just 
before  the  discount  period  overlaps  the  date  of  the  previous  cut. 
A  similar  fluctuation  in  value  occurs  in  the  case  of  an  account 


THE  VALUATION  OF  FORESTS 


93 


94  FOREST  VALUATION 

in  a  savings  bank  from  which  the  accumulated  interest  is  with- 
drawn, say  every  10  years.  For  land  which  is  bare  of  trees  but 
in  condition  to  be  planted  at  once,  the  period  intervening  to 
reduce  the  value  of  this  prospective  income  coincides  with  that 
for  growth  of  the  crop.  But  should  the  land  first  require  drain- 
ing, or  other  preparation  as  in  the  case  of  peat  lands  or  shifting 
sands,  a  still  further  shrinkage  of  prospective  value  occurs,  be- 
cause of  the  lengthened  time  and  extra  expense  intervening. 

This  discounted  value  of  future  income,  computed  for  a  date 
just  previous  to  the  origin  of  an  even-aged  stand  of  timber, 
gives  the  value  of  forest  land  bare  of  trees. 

This  value  is  obtained  from  Formula  C,  by  omitting  the  value 
of  the  timber  Y.  Let  Sv  =  expectation  value  of  forest  land. 

(E) 


Then 

o         Y-C 

(C  +  E), 

kjv  — 

i.opn—  i 

or 

Y  +  TP(i.o 

pn-p)   +  Tq(l.0pn~ 

0  +  Tr(i.op 

S,.= 

-C-Cd(i.c 

>pn-d}-Ce(i.opn-e} 

-Cf(iopn-f) 

,or  - , 

S,,  the  expectation  or  capital  value  of  forest  land  bare  of  trees, 
may  be  likened  to  the  value  of  bare  land  suitable  for  farm  crops 
or  orchards.  In  the  case  of  farm  land,  it  may  happen  that  the 
sale  value  of  one  annual  crop  will  equal  or  exceed  the  value  of 
the  land,  and  farms  are  usually  sold  subject  to  crop  removal 
or  in  the  winter.  With  orchards,  the  value  of  the  bearing  trees 
greatly  enhances  that  of  the  bare  soil.  Even  a  young  orchard 
increases  land  values.  In  the  latter  case,  it  is  of  small  moment 
whether  value  is  separated  into  the  value  of  the  land  and  that 
of  the  fruit  trees,  for  both  are  sold  together.  With  forest  trees, 
the  relation  between  land  values  and  ultimate  income  is  exactly 
the  same,  but  the  period  covered  by  the  growth  of  the  stand  is 
so  long  that  one  is  apt  to  lose  sight  of  the  fact  that  this  so- 
called  value  of  land  is  merely  the  discounted  value  of  the  future 
crops  of  timber. 

This  soil  value  Sv  represents  the  value  of  all  future  income 
dating  from  a  point  just  subsequent  to  the  complete  removal  of 


THE  VALUATION  OF  FORESTS  95 

a  crop  of  timber.     It  is  the  value  of  all  future  crops  exclusive 
of  the  one  occupying  the  ground. 

But  Sv  represents  this  value  correctly,  only  for  the  year  of 
cutting,  or  just  previous  to  planting.  Dismissing  the  idea  that 
Sv  represents  the  actual  "intrinsic"  value  of  the  soil  itself,  and 
regarding  it  solely  as  the  discounted  net  value  of  the  future  re- 
ceipts from  timber,  it  is  seen  that  this  value  Sv  holds  good  only 
for  the  one  year.  Just  previous  to  the  cut,  the  property  is  worth 
F  +  51,,.  Just  subsequent  to  cutting,  the  value  is  Sv.  But  when 
this  net  income  is  discounted  to  any  previous  year  a,  its  value 

£ 

ceases  to  be  Sv  and  becomes  — The  value  of  the  entire 

i.opn~a 

property,  soil  and  timber,  as  determined  from  the  net  revenue 
(see  §  112,  Formulae  BI  and  B2),  is  the  sum  of  the  net  income 

from  the  standing  crop  plus  the  discounted  net  income  from 

^ 

future  sources,  represented  by  • ^  •     The  value  of  the  stand- 
ing timber  is IE 

i.opn  a      \         i.opn 

The  sum  is,  therefore, 

Y  +  S,  +  E_E 
i.opn~a 

But  since  Sv  reappears  every  n  years  as  the  net  value  of  bare 
soil,  it  may  be  assumed  that  this  represents  the  value  of  the  soil 
during  the  intervening  period,  and  that  the  excess  of  value  for 
the  property  represents  the  value  of  the  trees  or  growing  stock. 
Under  this  assumption,  Sv  might  be  regarded  as  the  fixed  capi- 
tal, corresponding  to  a  sum  of  money,  and  the  value  of  the 
timber  as  the  accumulating  interest  earned  by  this  capital. 

To  determine  what  annual  interest  this  soil  capital  is  earning, 
it  is  necessary  merely  to  multiply  Sv  by  the  rate  of  interest  p 
used  in  calculating  it. 

Sv  X  o.op  =  soil  rent  (§  162).  (£2) 

Expectation  value  of  soil  is  merely  an  expression  of  net  income. 
Instead  of  being  permanent  or  fixed,  it  is  a  prediction  or  forecast, 
and  changes  'constantly  (as  do  all  values)  not  only  with  every 


96  FOREST  VALUATION 

change  in  economic  conditions  affecting  the  price  of  products, 
but  with  the  opinions  of  property  owners  as  to  the  amount  and 
present  value  of  the  anticipated  income.  Since  it  is  the  furthest 
removed  from  actual  income,  soil  value  is  the  most  unreliable  of 
all  forest  values,  and  is  subject  to  greater  proportional  fluctua- 
tions than  values  of  standing  timber. 

117.  Value  of  Many-aged  Forests  Producing  Regular  In- 
come. —  The  true  character  of  this  capital  value  of  bare  forest 
soil  is  further  emphasized  in  the  valuation  of  stands  of  timber 
composed  of  trees  of  many  different  ages. 

Two  cases  may  be  presupposed.  First,  the  existing  age  classes 
are  so  distributed  that  an  amount  of  timber  can  be  cut  at 
equal  intervals  of  time,  and  of  approximately  equal  quantity 
and  value.  Second,  the  age  classes  are  irregular  in  quantity 
and  unevenly  distributed  as  to  age.  This  second  example  is 
the  prevalent  type  of  many-aged  forest. 

In  neither  case  is  the  land  ever  clear  of  timber,  unless  the  young 
age  classes  are  destroyed  by  fire  or  logging.  It  follows  that  for 
a  forest  of  this  character  the  value  of  bare  land  cannot  be  deter- 
mined, except  by  making  an  artificial  assumption  of  an  even- 
aged  stand  of  equal  total  yield  with  that  of  the  many-aged 
forest,  and  in  which  the  trees  take  an  equal  time  to  develop. 
But  the  trees  in  the  all-aged  stand  take  longer  to  grow  than 
they  would  if  even-aged,  on  account  of  suppression  or  shading. 
The  correct  determination  of  soil  value,  apart  from  the  stand, 
for  such  forests  is  therefore  quite  unsatisfactory.  With  a  slow- 
growing  species  the  values  indicated  for  bare  soil  may  be  nega- 
tive and  are  usually  very  low. 

But  the  forest  itself,  or  total  property,  both  soil  and  timber, 
even  after  a  cutting  has  just  been  made,  has  a  positive  and  often 
a  high  value. 

Whether  the  interval  between  cuttings  m  is  long  or  short, 
the  value  of  the  forest  just  after  the  cut  is 


But  in  this  case,  the  formula,  although  similar  to  that  (E)  for 


THE  VALUATION  OF   FORESTS  97 

bare  soil,  differs  in  the  period  m  and  gives,  not  the  value  of  soil, 
but  of  the  soil  and  timber  remaining  after  the  cut.  It  is  the 
value  of  the  real  estate  or  forest. 

The  term  Fv  is  thus  used  to  indicate  the  value  of  the  forest 
just  following  a  cut. 

For  any  year  previous  to  a  cut,  the  value  of  the  property  may 
now  be  found  by  discounting  the  net  value  of  this  yield  to  the 
present,  and  adding  the  discounted  value  of  Fv. 

This  gives 


i.opm~a  i.opm 


The  value  of  a  forest  producing  a  regular  annual  income  is 

found  by  capitalizing  this  net  income,  using  Formula  XII,  --  . 

o.op 

The  annual  income  will  be  Y  +  Tp  +  Tq  +  Tr. 

Annual  expenses  are  C  +  n  X  e,  since  e  is  the  annual  expense 
for  but  one  area  or  age  class  and  there  are  n  age  classes  in  the 
forest. 

Other  expenses,  as  Cd,  Ce  and  Cf,  also  occur  annually. 

p   _  Y  +  Tp  +  TQ  +  Tr  -  (C  +  Cd  +  Ce  +  Cf  +  n  X  e)     ,p  , 
v  o.op 

The  net  income,  which  is  thus  capitalized  to  obtain  value,  is 
termed  the  forest  rent  (§  162). 

118.  Value  of  Many-aged  Forests  Producing  Irregular  In- 
come. —  Should  the  value  of  irregular  many-aged  forests  be 
sought,  the  period  must  first  be  determined,  which  is  required 
by  the  average  trees  to  become  merchantable.  The  stand  must 
then  be  roughly  grouped  into  its  age  classes,  and  the  approxi- 
mate per  cent  of  total  area  agreed  upon  which  each  age  class 
occupies.  Each  of  these  yields  must  then  be  discounted  to  the 
present,  with  a  value  determined  by  its  area.  To  get  the  net 
value  of  each  crop,  the  future  expenses  must  be  pro-rated  ac- 
cording to  the  same  distribution  of  area.  Finally,  the  total  value 


98  FOREST  VALUATION 

is  obtained  if  each  yield  is  treated  as  a  recurring  rental  (Formula 
X,  Diagram  II).     An  example  of  such  a  valuation  would  be: 

Crops  cut  z 

in  year  a,  -  total  area, 

in  year  b,  -  total  area, 

in  year  c,  -  total  area. 

z 

If  total  value  of  all  crops  is  Y  and  total  expense  e  is  capital- 
ized as  E,  and  there  is  no  expense  for  reproduction,  the  value  of 
the  forest  is: 

-  (i.opn-°)  +-(i.<#*-»)  +  -  (i.opn~c) 
•F9-*- J- E. 


Should  an  expense  for  reproduction,  C,  occur  at  the  time  of 
cutting,  or  any  other  initial  expense  be  incurred  at  that  time, 
this  expense  is  subtracted  from  Y  in  that  year. 

As 

V       C  V  —  C  V  —  C 

-  - 


•Fv  =  —  -  -  -  -  --  E. 

i.  op    —  i 

(F.) 

Formulae  are  merely  convenient  methods  of  calculating  re- 
sults after  the  facts  are  obtained.  Any  large  area  of  forest 
requires  careful  analysis  and  separation  into  its  component 
parts  before  any  of  the  methods  of  computing  value  can  be 
applied. 

119.  Value  of  Timber  Separate  from  Land.  —  When  for  any 
reason  the  value  of  the  timber  must  be  separated  from  the  value 
of  bare  land,  it  may  be  done  by  subtracting  this  latter  value 
Sv  from  the  formulae  giving  the  total  value  of  the  property. 
Formula  D2  then  becomes 


THE  VALUATION  OF  FORESTS  99 

and  Formula  FI  reads 


provided  in  this  case  that  the  value  of  the  soil  can  be  determined 
or  agreed  upon  apart  from  that  of  the  poles,  saplings  and  seed- 
lings which  increase  the  value  of  F,  over  that  of  Sv. 

For  a  normal  forest  (§  109)  producing  annual  income,  the  ex- 
pectation value  of  the  standing  timber,  separate  from  the  land, 
may  be  found  by  subtracting  n  X  Sv  from  Formula  F%  which  then 
reads 


.op 


CHAPTER   VIII 
FOREST  STATICS  — THE  BALANCE  SHEET  —  PROFITS 

120.  Determining  the  Profits  of  a  Forest  Investment.— Forest 
statics  is  defined  by  Schlich*  as  "the  science  which  weighs  and 
considers  the  comparative  merits  of  the  different  methods  of 
treatment  to  which  forests  may  be  subjected.  The  financial  re- 
sults, or  income-yielding  power  of  an  undertaking,  are  expressed 
by  the  proportion  existing  between  the  yield  and  the  capital 
which  produces  it." 

Two  distinct  methods  are  possible  in  preparing  a  financial 
statement  in  forestry  (§73).  The  first  may  be  termed  the  spe- 
cific balance  sheet  and  conforms  to  the  principles  of  accounting, 
by  recording  only  the  actual  cash  investments  as  credits,  and 
valuing  the  assets  preferably  at  actual  cost.  By  means  of  the 
supplementary  profit  and  loss  account,  the  net  income,  or  loss, 
is  annually  transferred  to  the  balance  sheet. 

This  specific  balance  sheet  does  not  reveal  profits  until  they 
are  actually  realized.  It  is  therefore  extremely  conservative. 
For  a  business  based  on  deferred  income  as  in  forest  production, 
the  annual  net  deficit  of  expenses  over  income  may  continue  for 
many  years,  requiring  continuous  increase  in  invested  capital, 
which  would  be  further  increased  by  borrowing,  and  adding  to 
expense  the  actual  cost  of  interest  on  these  borrowed  funds. 
The  balance  sheet  indicates  an  increasing  deficit,  up  to  the  time 
the  timber  is  cut. 

With  the  receipt  of  this  income,  the  total  assets  are  suddenly 
increased  to  several  times  the  total  investment,  showing  an  ap- 
parent profit  of  hundreds  of  per  cent  in  case  of  even-aged  stands 
harvested  after  from  40  to  60  years. 

"  Manual  of  Forestry,"  Volume  III,  Forest  Management,  by  Sir  William 
Schlich,  4th  Ed.,  Chapter  VI,  p.  149.  Bradbury,  Agnew  Co.,  Ltd.,  10  Bouverie 
St.,  London.  1911. 

100 


FOREST   STATICS  — BALANCE   SHEET  — PROFITS  IOI 

Such  results  evidently  do  not  fully  accomplish  one  important 
purpose  of  a  balance  sheet,  which  is  to  reveal  to  the  owner  the 
true  financial  status  of  his  investment.  Two  elements  of  eco- 
nomic importance  have  been  neglected,  which  entirely  alter  this 
status.  The  expectation  value,  not  the  cost  of  the  assets,  is 
the  true  measure  of  the  debit  entries,  while  the  profits  finally 
credited  are  not  revealed  in  their  true  relation  to  costs  unless  the 
time  required  to  earn  these  profits  is  given  proper  weight  in 
the  balance  by  exhibiting  the  interest  at  p  per  cent  which  should 
have  been  earned  on  the  invested  capital  during  the  period. 

A  statement  which  includes  these  two  factors,  expectation 
value  and  interest  on  costs,  may  be  termed  the  "economic  fore- 
cast." Revaluation  of  assets  to  coincide  with  present  value 
rather  than  cost  is  practiced  in  commercial  accounting  when 
circumstances  seem  to  justify  it  (§  73).  But  the  addition  of 
unearned  interest  as  a  cost  is  universally  excluded  in  specific 
accounts.  The  economic  forecast  would  include  such  interest 
on  costs,  for  in  no  other  way  can  the  owner  inform  himself  of 
the  relative  value  of  the  profits  derived  from  income,  or  whether 
there  is  any  enterpriser's  gain.  The  apparently  enormous  final 
profits  shown  by  the  specific  balance  sheet  may,  when  tested  by 
this  economic  comparison,  be  revealed  as  equivalent  to  less  than 
p  per  cent,  which  is  no  profit  at  all  as  measured  by  the  standard 
of  enterpriser's  gain  (§42). 

In  this  economic  statement  the  proprietary  side  ordinarily 
shown  as  credit  is  excluded  altogether,  and  the  costs  are  shifted 
to  the  right-hand  column  in  order  to  compare  them  with  actual 
value  (§  73),  and  reveal  potential  profit  or  loss.  The  statement 
formulated  in  this  manner  is  thus  purely  impersonal,  and  does 
not  distinguish  between  borrowed  and  personal  capital.  It  is 
similar  to  that  which  would  be  formed  by  comparing  a  cost 
account  for  manufactured  articles,  as  credit,  with  the  sale  value 
of  the  article  as  debit.  But  in  the  case  of  productive  property, 
this  comparison  must  be  made  far  in  advance  of  the  receipt  of 
final  or  total  income  and  is  a  balancing  of  cost  against  expecta- 
tion value  for  the  entire  enterprise. 

That  the  economic  statement  will  show  entirely  different 


102  FOREST  VALUATION 

results  from  the  specific  balance  sheet  is  evident.  When  the 
accountant  insists  on  retaining  land  and  timber  in  the  balance 
sheet  at  their  original  cost,  the  credits  will  exceed  the  debits 
by  the  amount  of  annual  expenses  not  entered  as  a  capital  ex- 
penditure. This  deficit  is  further  increased  by  interest  paid 
on  borrowed  capital  if  such  expense  has  been  incurred.  By 
contrast,  the  economic  statement  shows  an  even  greater  "cost," 
since  interest  is  added  as  a  cost  item  to  all  capital  invested, 
whether  borrowed  or  not.  The  assets,  on  the  other  hand,  are 
treated  without  any  regard  for  actual  cost,  their  value  being 
determined  entirely  on  the  basis  of  future  income  (Chapter  VII). 
The  value  of  forest  property,  which  is  used  in  the  economic 
statement,  is  its  expectation  or  capital  value,  until  it  reaches 
maturity,  when  the  capital  value  of  the  standing  timber  is 
merged  in  the  sale  value  from  which  it  is  derived.  The  com- 
parison for  timber  property  at  any  year  previous  to  maturity 
of  the  timber  will  show. 


Debits. 

Credits. 

Expectation  value  of 
property,  consisting  of 
Young  timber, 
Forest  soil. 
Indicated    or    potential 
loss. 

Cost  of  property,  consisting  of 

8S3SH.H"*'* 

Interest  on  all  items  of  cost. 
Indicated  or  potential  profits. 

The  economic  forecast  in  forestry  thus  consists  of  balancing 
past  costs,  with  compound  interest  to  date,  against  future 
income  (§  62)  discounted  to  date,  as  represented  by  expectation 
value  of  assets.  By  thus  comparing  the  relative  values  of  past 
net  outlay  and  future  net  income,  for  any  year  a,  the  exact 
economic  status  is  revealed  for  that  date. 

This  method  of  valuation  for  forest  assets  may  be  compared  to 
the  appraisal  of  the  'property  and  business  of  a  lumber  company 
for  purpose  of  sale.  Cost  would  not  finally  determine  the  value 
placed  upon  any  item  of  such  property.  The  mill  and  logging 
road,  machinery  and  stock,  would  be  valued  on  the  basis  of 
their  future  usefulness  to  the  purchaser  and  present  owner. 
The  timber  would  be  appraised  at  going  prices  for  equally 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS  103 

good  stumpage.  Should  the  sale  be  consummated  these  ap- 
praised values  are  realized,  and  the  profit  shown  in  this  tenta- 
tive or  economic  statement  becomes  an  actual  profit,  entered 
specifically  on  the  books. 

To  what  extent  the  value  of  assets  in  a  specific  balance  sheet 
should  be  increased  above  cost  of  purchase,  is  a  question  to  be 
determined  by  the  character  of  the  business.  Unless  these 
increased  values  are  eventually  realized,  the  profit  shown  by 
reason  of  such  increase  exists  merely  in  anticipation,  and  until 
it  is  secured,  this  profit  cannot  be  distributed  as  dividends. 

There  is  considerable  difference  between  the  financial  status 
of  a  lumber  company  conducting  an  extensive  operation  with 
stumpage  held  merely  as  a  timber  mine  to  furnish  wood  until 
exhausted,  and  that  of  a  forest  owner  engaged  in  growing  timber 
as  a  business.  The  former  concern  is  obliged  to  adhere  rigidly 
to  the  accounting  principles  commonly  accepted  in  business 
circles.  Its  timber  will  be  entered  at  cost,  unless  a  bond  issue 
is  floated,  when  it  is  customary  to  appraise  the  timber  at  its 
present  stumpage  value  and  to  make  a  far  more  complete  esti- 
mate of  its  amount.  Bonds  are  secured  by  value,  not  by  cost 
of  property  bonded.  The  interest  on  these  bonds  must  be  met 
annually  or  foreclosure  follows.  Taxes,  protection  and  interest 
are,  therefore,  formidable  items  of  expense  and  timber  must  be 
cut  each  year  to  produce  sufficient  income  to  cancel  these  costs 
for  the  entire  remaining  body  of  stumpage. 

But  because  of  these  conditions,  the  actual  status  of  the 
lumberman's  investment  tends  to  follow  a  similar  course  to 
that  of  an  investment  in  growing  timber.  The  first  years  will 
tax  all  the  resources  of  the  owners  to  keep  ahead  of  their  obli- 
gations. Need  for  income  is  urgent.  The  tendency  is  to 
greatly  increase  the  size  and  capacity  of  mills  and  operations. 
This  universal  tendency  causes  overproduction  of  lumber  and 
defeats  its  own  ends  by  lowering  prices. 

But  once  a  concern  has  weathered  this  initial  period,  and 
reduced  its  indebtedness  and  carrying  charges,  the  final  years 
of  the  operation  become  more  and  more  profitable.  It  follows 
that  those  operators  who  have  the  greatest  amount  of  capital 


104  FOREST  VALUATION 

behind  them,  and  who  do  the  least  borrowing  and  maintain 
operations  in  a  region  after  others  have  ceased,  reap  large  profits, 
while  the  small  investors,  or  firms  attempting  too  much  with 
limited  capital,  are  often  bankrupted  in  the  first  stage  of  the 
business. 

The  investor  must,  therefore,  distinguish  sharply  between  the 
commercial  or  specific  trial  balance,  and  the  economic  forecast 
which  accounts  for  time,  includes  interest  on  the  investment  as 
a  cost,  and  bases  the  value  of  assets  not  on  cost  but  on  income, 
by  the  process  of  discount.  Such  a  "  balance  "  informs  the  owner 
of  his  true  economic  status,  thus  enabling  him  to  determine  his 
future  policy  —  whether  to  sell,  purchase  or  continue  to  operate. 
Economic,  and  not  specific,  profits  are  discussed  in  this  chapter. 

121.  The  Rate  of  Interest  in  its  Relation  to  Profits.  —  In 
securing  an  accurate  statement  or  balance  between  past  costs 
and  future  income  or  capital  value,  the  effect  of  the  element  of 
time  upon  such  relative  values  must  be  eliminated  or  equal- 
ized (§  u).  This  is  done  by  employing  the  same  rate  of  inter- 
est (§  38),  p  per  cent,  on  both  sides  of  the  equation. 

The  total  amount  of  compound  interest  is  increased  by  em- 
ploying a  higher  rate,  while  the  same  increase  in  the  rate  has 
the  opposite  effect  of  lowering  the  present  or  discounted  value 
of  assets.  This  effect  is  due  in  each  case  to  increasing  the 
difference  in  value  caused  by  the  element  of  time.  It  follows 
that  an  increase  in  the  standard  rate  of  interest,  p  per  cent, 
tends  to  obliterate  the  margin  of  profit  on  the  credit  side  of  the 
balance,  and  replace  it  with  a  debit  deficit  or  loss.  In  other 
words,  if  the  investor  is  satisfied  with  3  per  cent,  and  that  rate 
is  used  in  computing  values  for  the  balance  sheet,  the  statement 
might  indicate  a  profit,  but  if  he  uses  6  per  cent  as  the  necessary 
basis  of  comparison  with  other  investments,  the  resulting  bal- 
ance may  indicate  a  loss,  although  the  cash  income  and  expenses 
remain  the  same  in  either  case.  The  change  is  wrought  wholly 
in  discount  or  expectation  value  and  in  the  accumulated  "cost  " 
of  compound  interest. 

A  rate  of  interest  may  be  found  for  any  given  total  of  expense, 
on  the  one  hand,  and  of  income,  on  the  other,  which  will  just  bal- 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS  105 

ance  the  cost  or  credit  side  with  the  asset  or  debit  side  of  the 
balance  sheet.  This  rate  would  in  most  instances  include  a 
fraction  or  decimal,  such  as  4.27  per  cent.  The  rate  which 
thus  balances  cost  and  income  is  the  rate  of  interest  earned  by 
the  investment.  And  since  money  is  never  borrowed  at  odd 
rates,  and  the  earning  power  of  an  investment  does  not  deter- 
mine the  rate  of  interest  used  in  calculating  its  value  (§62), 
these  items  of  cost  and  value  seldom  balance  exactly,  but  always 
show  a  profit  or  loss. 

Yet  the  fact  that  this  rate  exists  indicates  a  second  method 
of  determining  enterprisers'  profits.  The  rate  earned,  expressed 
in  terms  of  compound  interest,  eliminates  the  element  of  time 
as  effectually  as  does  discount,  and  enables  the  investor  to  com- 
pare the  income  rather  than  the  expectation  value  of  two  in- 
vestments. The  forest  investment  must  earn  p  per  cent  before 
it  becomes  as  desirable  as  the  money  it  represents.  If  x  per 
cent  is  earned,  then  when  *  per  cent  >  p  per  cent  the  excess 
represents  the  ratio  of  profit  or  enterpriser's  gain,  per  dollar 
of  investment,  in  excess  of  the  standard  rate.  If  x  per  cent 
<  p  per  cent,  the  rate  x  per  cent  still  indicates  net  income, 
but  compared  with  p  per  cent,  there  is  a  loss,  or  rather  a  failure 
to  realize  the  amount  desired. 

122.  Profits  in  Destructive  Lumbering.  —  It  is  assumed  that 
owners  who  do  not  intend  to  continue  in  forest  production  will 
sell  the  land  or  devote  it  to  some  other  purpose.  Its  sale  or 
appraised  value  for  this  purpose  is  credited  as  income. 

Let  P  =  profit. 

P  =  Y  +  S8  -  (C  +  Sc)  i. op*  -  E  (i.op»  -  i) 

=  7  +  S,  +  E  -  (C  +  Sc  +  E)  i.op».  (H) 

This  formula  is  expanded,  by  the  addition  of  other  items  of 
both  cost  and  income,  to  the  form, 

P  =  Y  +  SS  +  E  +  TP  (i.o/>»-»)  +  Tq  (i.c#»-«) 
+  Tr  (i.opn~r)  -(C  +  SC  +  E)  i. op" 
-  Cd  (i.opn~d)  -  Ce  (i.o^-')  -  Ct  (i.o^-O-    (HO 

This  formula  gives  the  profit  on  a  single  stand  of  timber, 
for  the  year  of  sale,  assuming  that  both  timber  and  land  are 


106  FOREST  VALUATION 

sold,  or  that  the  timber  is  immediately  removed  and  the  land 
sold  or  appraised. 

Actual  profits  on  the  investment  in  land  and  timber  exclusive 
of  lumbering,  for  a  large  operation,  must  be  based  on  actual 
sale  of  land  rather  than  appraisal  at  time  of  sale  of  timber, 
and  if  this  sale  is  delayed,  as  it  may  be,  for  many  years,  the 
transaction  is  not  closed.  A  new  account  may  be  opened  for 
the  denuded  land,  crediting  it  to  the  original  account  preferably 
at  the  cost,  not  the  present  sale  value  of  land,  and  debiting 
the  land  account  with  this  investment.  If  a  "cost"  account  is 
kept  as  before,  the  land  will  be  charged  with  interest  until  sold. 

123.  Profits  on  a  Stand  of  Timber.  —  Whether  or  not  the 
owner  intends  his  land  for  future  crops  of  timber,  the  profit  on 
the  existing  stand  may  be  separately  stated,  by  charging  interest 
on  the  cost  of  land  as  an  expense  against  the  timber,  and  credit- 
ing the  land  at  its  original  cost,  when  the  timber  is  sold. 

p  =  7  +  Sc  -  (C  +  Sc}  i.opn  -  E  (i.opn  -  i) 

=  7  +  Sc  +  E  -  (C  +  Sc  +  £)  i.op».  (K) 

This  formula  differs  from  H  only  by  the  introduction  of  Sc 
as  an  asset  in  place  of  SS)  and  may  be  expanded  in  the  same 
manner  as  HI. 

124.  Anticipated  Profits  on  Young  Timber.  —  Assuming  that 
Sc  is  credited  at  the  time  the  timber  is  cut,  the  profits  of  that 
year  may  be  anticipated  for  the  year  a  in  one  of  two  ways. 
The  net  profit  (K)  may  be  discounted  to  the  present  (II),  or 
the  balance  may  be  struck  for  the  given  year  by  direct  compu- 
tation of  value  and  cost  for  that  year.     In  the  latter  case, 


Cost  =  (C  +  Sc  +  E)  i.opa  -  (Sc  +  £). 

P  =  Y  +o^+  E  -  (C  +  Sc  +  JE)  i.o/>".          (KO 

This  formula  may  be  expanded  by  the  addition  of  income 
and  cost  items,  regardless  of  whether  these  costs  occur  after 
the  year  of  valuation,  or  income  occurs  previous  to  this  year. 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS  107 

The  expression ^  gives  the  present  equivalent  of  Tp  in  the 

year  a  whether  a  >  p  or  the  reverse.     Therefore, 


Tp  TQ  Tr 

i  .opn~a  i  .opp~a      i  .op*'*      i  .of 

-  (C  +  Sc  +  E)  i.opa  -  Cd 


c  p 

i  .op~a 


f~>    /•      —  Aa— e\    /""    fT  r\faa—f\  (~[£   ^ 

125.  Profits  from   Continuous  Forest  Production.  —  If  in- 
stead of  abandoning  the  business,  forest  production  is  to  be 
continued,  the  sale  value  St  credited  for  land  does  not  express 
the  true  conditions.     The  value  S,,  representing  the  expectation 
value  of  the  soil  or  the  value  of  all  future  crops,  must  be  sub- 
stituted for  S,. 

Formula  H  then  becomes 

P  =  Y  +  Sv  +  E  -  (C  +  Sc  +  E)  i.op».  (L) 

The  net  profits  from  future  crops,  expressed  as 

Y  -C 
i. op*  -  i 

may  be  substituted  for  the  expression  Sv  in  the  formula,  which 
does  not  alter  the  result.  Both  the  net  profit  on  the  present 
crop,  and  on  the  future  crops,  Sv,  should  include  all  items  of 
cost  and  income  which  appear  in  Formula  HI,  but  the  repetition 
of  these  terms  in  Formula  L  has  been  omitted. 

126.  Anticipation  of  Continuous  Profits.  —  To  anticipate  the 
total  net  profit,  for  the  year  a,  including  net  income  from  all 
future  crops,  the  value  S,,  once  determined,  is  substituted  for 
Sc  as  an  asset  in  Formula  KI  which  then  reads 


i.op. 


This  formula  is  modified  by  the  same  additions  for  extra  items 
of  cost  or  income,  as  Formula  K2.  But  Formula  KI  gives  the 
profit  on  the  present  stand  of  timber,  exclusive  of  future  crops 
or  of  profit  on  the  sale  of  the  land,  while  LI  includes  these 


108  FOREST  VALUATION 

future  profits.     Should  Formula  LI  be  derived  in  the  same  way 
as  KI  the  result  stands 


"  (Sv  ~ 


which  indicates  a  means  of  separating  the  profits  on  the  stand- 
ing timber  from  that  on  the  future  crops,  or  "soil,"  parallel  to 
the  method  employed  for  sale  values  in  §  123. 

The  true  derivation  of  Formula  LI  is  from  value  (§  116,  D2) 
and  cost  (§105,  A2)  of  the  entire  property,  timber  and  soil. 

Then 

P  =  aFv-  °FC.  (U) 

127.  Profits  Expressed  in  Soil  Values.  —  In  the  year  in 
which  the  enterprise  of  planting  or  reproduction  is  undertaken, 
and  previous  to  the  actual  planting,  the  net  value  of  all  future 
income  is  Sv,  or,  expressing  this  value  as  discounted  from  future 
crops,  it  equals 

V  —  C 


i.  op"  -  i 

The  cost  includes  merely  the  price  paid  for  the  soil  5C.     Then, 
P  =  Sv  -  Se.  (L3) 

Since  this  profit  is  shown  for  the  year  previous  to  undertaking 
forestry,  it  is  taken  as  an  indication  of  the  advisability  of  such 
an  enterprise.  This  relation  shows  clearly  the  nature  of  Sv, 
which  is  merely  a  calculation  of  discounted  net  income.  Sv 
does  not  indicate  what  a  purchaser  should  pay  for  land.  It 
indicates  the  highest  price  which  he  can  afford  to  pay  and  still 
expect  to  earn  the  desired  rate,  p  per  cent,  on  his  undertaking.  If 
more  than  this  is  paid,  a  prospective  loss  is  incurred,  i.e.  he 
cannot  expect  to  earn  as  much  as  p  per  cent.  If  the  land  costs 
less  than  Sv  he  has  good  prospects  of  earning  a  profit  at  p 
per  cent,  or  a  rate  of  income,  x,  exceeding  p  per  cent  on  his 
investment.  If  a  purchaser  is  so  foolish  as  to  deliberately 
convert  his  expected  profits  (Sv  —  Sc}  into  costs,  by  making 
Sc  =  Sv,  he  is  merely  handing  over  these  profits  to  the  one  who 
sells  him  the  property. 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS  109 

Sv  increases  in  value  with  every  change  in  prospective  in- 
come or  expenses  which  alters  the  net  value  of  this  income, 
and  is  much  larger  for  soils  of  good  than  poor  quality.  But 
there  is  evidently  no  profit  in  devoting  to  forestry  lands  which 
will  sell  for  other  purposes  for  a  sum  larger  than  Sv. 

In  countries  where  forestry  is  extensively  practiced  on  lands 
owned  by  states,  or  on  private  estates  which  have  practically 
never  changed  hands,  there  is  no  way  of  determining  the  cost 
of  land.  The  value  of  the  soil,  Sv,  is  calculated  for  the  pur- 
poses of  taxation  and  as  a  necessary  step  in  valuing  growing 
timber.  This  value  may  be  recalculated  at  any  time.  It  is 
evident  that  the  soil  value  may  always  be  placed  at  a  figure 
which  will  permit  the  investment  to  earn  exactly  the  rate  of  inter- 
est agreed  upon  as  the  standard  for  forest  investments.  And 
in  practice,  if  during  the  crop  period  it  becomes  evident  through 
price  changes  or  other  influences  that  the  investment,  with  its 
former  soil  value,  will  earn  more  than  p  per  cent,  this  value 
is  promptly  raised,  and  the  rate  of  earnings  is  thus  arbitrarily 
reduced  to  p  per  cent  once  more.  The  real  status  of  the  in- 
vestment is  thus  concealed  in  the  capitalized  value  of  the  soil. 
Applied  practically  to  a  private  operation,  this  process  would 
consist  of  entering  the  land  in  the  capital  account  as  an  asset 
having  a  value  in  excess  of  its  cost.  If  this  value  were  made 
great  enough,  the  investment  never  could  earn  more  than  p  per 
cent  upon  said  value.  But  figured  on  the  original  cost,  a  much 
greater  rate  of  profit  may  be  shown.  This  practice  of  capital- 
izing income  as  soil  value  is  universal  in  European  forest  finance, 
and  the  profits  of  forestry,  standardized  to  p  per  cent,  may  be 
discovered  only  by  comparing  the  values  of  land  computed  for 
different  sites  and  species,  and  by  a  knowledge  of  past  changes  in 
these  soil  values. 

If  S,  equals  Sc,  it  may  be  substituted  for  Sc  in  Formulae  A, 
AI  and  A2.  This  is  done  under  the  conditions  just  discussed, 
where  Sc  is  not  determinable.  The  effect  of  this  substitution 
is  to  make  the  computed  cost  of  timber  in  any  year  of  the  rota- 
tion just  equal  to  its  expectation  value  in  that  year,  and  to 
reduce  profit,  outside  of  soil  value,  to  zero. 


110  FOREST   VALUATION 

In  the  same  way,  it  can  be  shown  that  for  definite  costs  and 
income,  the  profit  determined  for  any  year  may  be  converted 
into  that  for  any  other  year  by  the  use  of  Formulae  I  and  II. 

Substituting  S,  for  Sc  in  Formula  LI,  thus  reducing  profit 
to  zero,  this  formula  becomes 

r  +  s.+E_ 


i.op 
Then 

Y+S+E_ 
i.opn 

Resuming  the  value  of  Se  as  cost  of  land,  the  profit  is 

P  =  Y  +  S*  +  E  _  (C  +  £)  -  sc 

I.  Op* 

=  SV-  Sc.     (See  L3.) 

Since  Formulae  LI  and  L3  are  thus  derived  from  Formula  L 
by  discount  (II),  the  reverse  is  true,  and  for  any  year  a 

P-(£-Sjinp-  CU) 

128.  Profits  Expressed  as  a  Ratio  of  Income  to  Capital.  — 

The  economic  forecast  shows  profits  as  a  net  sum  or  balance 
between  assets  and  cost,  which  sum  cannot  be  realized  in  money 
without  a  sale  of  ownership.  But  the  net  future  income  which 
is  accountable  for  this  balance  of  profit  shown  may  be  also 
expressed  in  terms  of  interest  earned  on  the  cost  instead  of  as 
capitalized  value  (§121).  The  rate  or  ratio  of  income  to  capital 
depends  directly  upon  the  period  of  time  elapsing  between  ex- 
penditure and  income  (§  23),  a  fact  often  lost  sight  of.  In  quick 
profits,  earned  largely  by  the  sale  of  property  at  an  advance  in 
capitalized  value  rather  than  by  awaiting  the  slow  realization 
of  income,  the  element  of  time  is  lost  sight  of;  yet  every  profit 
should  be  standardized  by  reducing  it  to  the  rate  of  interest 
which  it  represents  on  the  investment  for  the  period  of  waiting. 
Should  a  property  be  sold  at  double  its  cost,  the  profit  is 
100  per  cent  on  cost.  But  with  the  element  of  time  intro- 
duced, the  rate  earned  would  be  as  follows  (Formula  XIV)  : 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS 


Sale  at  end  of 

Rate  earned, 
percent. 

i  year 

100 

5  years 

14.9 

10  years 

7-2 

20  years 

3-6 

50  years 

i-4 

100  years 

•  7 

129.  Earning  Power  of  Capital  Invested  in  Forest  Produc- 
tion. —  In  no  form  of  business  does  the  per  cent  earned  by  the 
total  amount  of  capital  invested  equal  the  per  cent  earned  by 
the  proprietor's  investment  unless  he  furnishes  the  entire  capi- 
tal without  borrowing  (§32). 

In  business  receiving  annual  income,  the  capital  needed  to 
carry  the  current  expenses  is  usually  borrowed,  and  therefore 
does  not  share  in  the  profits  but  receives  p  per  cent  only. 

These  arguments  are  used  as  a  justification  for  separating  the 
capital  invested  in  a  forest  crop  into  two  portions,  one  of  which 
shall  be  computed  at  p  per  cent,  and  not  share  in  the  profits, 
while  the  remainder  is  the  basis  upon  which  the  rate  of  income 
is  computed.  By  thus  reducing  the  amount  of  profit-sharing 
capital,  the  rate  of  profit  is  increased  or  reduced  on  this  capital 
as  the  earnings  exceed  or  fall  below  p  per  cent  on  the  total  in- 
vestment. 

For  instance,  it  may  be  arbitrarily  assumed  that  the  owner 
acquires  the  land,  but  borrows  the  funds  needed  for  all  expenses 
of  crop  production  (Group  A,  §  104),  as  silvicultural  expenses, 
and  maintenance  or  annual  charges.  It  has  been  shown  that 
such  a  transaction  would  seldom  occur.  But  if  it  does,  these 
expenses  must  first  be  returned  from  income,  with  compound 
interest  at  p  per  cent.  The  remaining  sum  is  net  income 
earned  by  the  owner's  capital,  Sc. 

Net  earnings  =  Y  +  Sv  -  1C  (i.o#»)  +  E  (i.opn  -  i)f 
=  Y  +  Sv  +  E  -  (C  +  E)  i.opn. 


The  substitution  of  Sc  or  of  Ss  for  Sv  will  adjust  this  formula 
to  any  desired  condition  (§§122,  123  and  125). 


112  FOREST  VALUATION 

In  this  formula,  E  =  —  —  ,  and  as  p  is  determined,  this  term 
o.op 

has  a  definite  value  (but  see  Formula  N2). 

Capital  invested  by  owner  =  Se, 
Rate  earned  =  x  per  cent, 

Period  of  time  =  n  years. 

By  use  of  Formula  XIV  (§  89), 

Sc  (I.Q*»)  =  Y  +  Sv  +  E  -  (C  +  £)  i.o/>», 


or 


v-  .  ,„. 

i.oxn  =  —  -*~z  —  (N) 

Oc 


This  division  of  capital  is  purely  arbitrary.  An  equally 
justifiable  assumption  is  that  the  owner  also  invests  the  capital 
needed  for  silvicultural  operations  and  all  initial  expenses  (Group 
B,  §  104).  In  this  case,  the  borrowed  capital  E  is  first  repaid 
with  p  per  cent  interest  from  the  gross  income  and  x  per  cent 
determined  for  the  remainder. 

Net  earnings  =  Y  +  Sv  —  E  (i.opn  —  i), 

Capital  invested  by  owner  =  Sc  +  C. 

Then  (Se  +  C)  i.ox*  =  Y  +  Sv  +  E-E  (i.o/>»), 


Oc   T 


-E(i.op") 
- 

Both  of  these  solutions  (N  and  Ni)  give  a  value  for  x, 
greater  or  less  than  that  actually  earned  by  the  entire  capital 
investment.  The  difference  is  greatest  when  only  the  investment 
in  soil  is  used  as  a  basis.  Method  NI  has  been  advocated  for  use 
in  this  country.* 

The  true  "economic"  per  cent  (§121)  earned  by  an  investment 
is  the  rate  paid  on  all  capital  invested  for  periods  of  one  year  or 

*  Forest  Management  of  Loblolly  Pine,  Bulletin  n,  U.  S.  Department  of  Agri- 
culture, W.  D.  Sterrett,  Jan.  23,  1914,  p.  21. 


FOREST  STATICS  —  BALANCE   SHEET  —  PROFITS  113 

over,  regardless  of  ownership.  This  investment  must  include 
the  annual  expenses  which  are  not  cancelled  by  annual  income. 
In  this  case, 

Net  earnings  =  Y  +  Sv, 

Capital  invested  by  owner  =  Sc  +  C  +  n  (e)  (see  §  105). 

Then  net  earnings  =  Y  +  Sv  -  \(SC  + C  +  E)  i.oxn  -El, 

Y  +  Sv  +  E 
n  (N2) 


But  in  this  formula,  E  =  —  '—  ,  and  as  x  appears  on  both  sides 
o.ox 

of  the  equation,  a  solution  is  not  reached.  The  value  of  x  may 
be  obtained  by  trial.  A  trial  per  cent  x'  is  first  substituted  for 

x  in  the  expression  --    and  the  value  E'  determined.    The 
o.ox 

solution  then  gives  a  value  x".    This  new  value  is  then  sub- 

stituted for  x'  and  --  -  gives  E".     The  second  solution  of  the 
o.ox 

equation  will  give  a  value  for  x  usually  within  one-tenth  of  one 
per  cent  of  true  value. 

This  result  is  satisfactory,  for  the  rate,  x,  is  a  prediction  or 
estimate  in  most  instances;  or  where  results  are  at  hand,  it  is 
merely  a  calculation  intended  to  gauge  the  relative  merits  of 
the  investment  compared  with  others.  For  such  purposes,  even 
\  per  cent  is  sufficiently  close. 

In  the  solution  of  the  value  of  x,  the  use  of  logarithms  is  not 
usually  necessary.  The  value  may  be  found  in  Table  VI,  op- 
posite n  years,  and  interpolated  to  one-tenth  of  one  per  cent. 

This  method  of  gauging  the  profits  of  forest  production  is  far 
more  suitable  to  new  conditions  characteristic  of  the  industry 
in  America  than  the  method  of  capitalizing  income  in  the  form 
of  soil  value  or  computing  the  "forest  per  cent."  In  almost 
every  instance,  except  for  lands  owned  by  the  nation,  the  cost  of 
acquiring  the  property  is  known,  or  is  a  determining  factor  to 
be  decided  previous  to  undertaking  forestry.  It  is  upon  this 


114  FOREST  VALUATION 

investment  that  profits  must  be  computed  whether  or  not  the 
capital  invested  in  future  expenses  is  also  entitled  to  share  in  the 
profit.  The  rate  of  interest  earned  offers  an  intelligible  standard 
of  comparison  with  the  common  forms  of  business  enterprise. 

The  profit  (§  39)  or  enterpriser's  gain  is  then  found  as  a  ratio 
instead  of  a  lump  sum,  by  subtracting  p  per  cent  from  x  per  cent. 

European  methods  of  computing  the  rate  x  earned  by  capital 
invested  in  forestry  differ  from  those  advocated  above.  The 
capital  investment  is  regarded  as  the  cost  of  the  forest  soil, 
in  accord  with  Method  N.  But  instead  of  computing  the  rate 
of  compound  interest  which  is  earned  on  Sc,  the  first  step  is  to 
calculate  the  annual  "rent"  earned  on  Sv,  which  is  equivalent 
to  Sv  X  o.op.  This,  divided  by  Sc,  gives  o.ox,  and  x  is  termed 
the  mean  annual  forest  per  cent.  As  expressed  by  Schlich, 

x  =  |  X  p.  (N,) 

The  per  cent  x  in  this  formula  is  more  sensitive  than  in 
Formula  N.  When  x  >  p,  a  higher  rate  is  shown  for  x  than  that 
given  by  method  N.  This  is  due  to  the  effect  of  using  different 
rates  of  interest,  x  versus  p,  in  discounting  by  the  two  methods. 

Formulae  N  to  N3  express  profits  only  for  the  beginning  of 
the  enterprise,  as  forecasts  or  as  summaries.  When  the  poten- 
tial annual  or  current  rate  of  interest  is  desired,  termed  the  cur- 
rent annual  forest  per  cent,  this  may  be  found,  after  the  timber 
becomes  of  merchantable  value,  by  first  determining  the  annual 
increase  in  this  stumpage  value  (Chapter  XII,  §  182). 

Let  Yn  =  stumpage  value  in  year  n. 

Yn+i  =  stumpage  value  in  year  n  +  i. 

From  the  increase  thus  shown  must  be  deducted  the  annual 
expenses  e.  The  investment  consists  of  the  cost  of  the  forest 
for  the  year  n,  consisting  of  soil  and  timber,  and  represented 
(Formula  A2)  by  aFc. 

The  formula  for  current  forest  per  cent  is 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS     115 

for  which  may  be  substituted 


For  a  normal  forest  (§  109)  the  forest  per  cent  is  obtained  by 
methods  identical  with  those  applied  in  Formulae  N3  and  N4.  The 
value  of  such  a  forest  (F2)  divided  by  its  cost,  which  is  either 
the  cost  of  purchase  or  of  production  (§  109),  gives  the  basis  for 
the  following  formula 

(N6) 


130.  The  Relative  Importance  of  Profits  in  Private  versus 
Public  Forestry.  —  In  Chapter  III  it  was  emphasized  that  for 
very  long  periods  the  operation  of  the  laws  of  compound  in- 
terest requires  the  lowering  of  the  rate  of  interest,  "p  per  cent," 
used  to  gauge  the  relative  value  of  investments.  It  is  easily 
shown  that  enterprises  running  for  periods  of  over  50  years 
cannot  earn  to  exceed  4  per  cent  except  under  the  most  favor- 
able circumstances,  although  the  specific  net  profits  above 
cash  outlay  may  exceed  this  outlay  by  several  hundred  per 
cent  (§§53  and  128). 

Private  industry  cannot  be  expected  to  undertake  the  business 
of  forest  production  on  a  scale  commensurate  with  our  future 
needs,  lor  the  following  reasons: 

1.  A  higher  rate  of  interest  is  required  on  private  than  on 
public  undertakings. 

2.  The  average  business  life  of  an  individual  is  shorter  than 
the  period  required  to  produce  a  forest  crop. 

3.  The  private  enterprise  depends  for  its  existence  solely  on 
profits,  while  the  public  undertaking  includes  the  benefit  to  the 
community  as  the  principal  item  of  income,  and  may  therefore 
be  conducted  at  an  actual  money  loss  and  still  be  justified. 

4.  In  many  instances,  lands  are  already  the  property  of  the 
state  or  nation,  and  no  cost  or  interest  on  land  need  be  charged. 
The  sole  cost  of  public  forestry  in  such  instances  is  the  sum  of 
actual  outlays  for  protection  and  silvicultural  measures. 

5.  Public  forestry  can  and  should  be  conducted  on  a  very 


Il6  FOREST  VALUATION 

large  scale  as  it  is  on  the  national  forests,  with  resulting  economy 
in  all  measures  of  protection,  technical  administration  and 
improved  efficiency  which  will  increase  future  revenue. 

6.  Private  ventures  are  based  on  the  assurance  of  an  enter- 
priser's gain  or  net  profit  above  p  per  cent,  which  is  a  matter 
of  indifference  in  public  enterprises.  The  necessary  lowering 
of  the  interest  rate  on  long  investments,  the  postponement  of 
results  and  the  increasing  importance  of  the  governing  rate  of 
interest  as  affecting  the  size  of  the  indicated  profits  lessen  the 
individual's  interest  in  forest  production  as  a  business  venture, 
and  strengthen  the  reasons  for  state  or  national  enterprise. 

After  the  forest  capital  has  been  destroyed,  its  restoration  by 
planting  or  seeding  can  be  of  interest  to  private  owners  only 
for  species,  regions  and  sites  which  promise  reasonably  quick 
returns  and  high  values,  such  as  are  shown  for  white  pine  in  New 
England  or  Loblolly  pine  in  Maryland.  But  before  destructive 
lumbering  has  made  such  restoration  necessary,  especially  for 
forests  which  show  a  succession  of  age  classes,  such  as  spruce  in 
the  northeast,  the  private  owner  may  often  continue  to  operate 
indefinitely,  with  profit,  by  removing  only  the  more  mature 
timber.  This  difference  is  due  to  the  fact  that  such  a  forest 
produces  income  annually  with  which  to  cancel  expenses.  Under 
such  circumstances  the  specific  balance  sheet  shows  an  annual 
profit;  there  is  no  accumulation  of  unpaid  interest,  and  by  fore- 
going the  "profits"  he  might  obtain  at  any  time  by  withdrawing 
the  entire  capital,  the  owner  substitutes  a  permanent  annual 
income. 

In  considering  questions  of  public  policy,  no  sound  conclusions 
can  be  reached  if  the  financial  questions  involved  are  neglected. 
The  difficulties  of  inducing  private  owners  to  voluntarily  enter 
forest  production  as  a  definite  business  are  evident.  If  this 
course  is  made  mandatory  by  legislation,  as  is  seriously  contem- 
plated in  some  states,  it  must  first  be  shown  that  the  expenses 
thus  required  are  in  reasonable  relation  to  the  income  that  can 
be  expected  from  forestry.  Otherwise  it  would  appear  that  the 
state  is  attempting  to  shift  onto  private  shoulders  a  responsibility 
which  it  should  publicly  assume. 


FOREST  STATICS  —  BALANCE  SHEET  —  PROFITS     117 

This  public  sentiment  for  regulation  is  the  expression  of  an 
instinctive  protest  against  destructive  lumbering  as  a  policy, 
for  it  is  far  more  expensive  and  wasteful  to  tear  down  a  busi- 
ness and  then  rebuild  it  than  to  continue  it  as  a  going  concern. 
Whether  or  not  forest  owners  can  afford  any  other  policy  than 
destructive  lumbering,  they  should  in  any  case  use  every  effort 
to  do  as  little  harm  as  possible  to  reproduction,  protect  cut-over 
lands  from  fire,  and  induce  the  formation  of  a  new  crop  of  natural 
seedlings  on  absolute  forest  soils.  In  proportion  to  the  effective- 
ness of  such  measures  for  perpetuating  the  productiveness  of 
forest  lands  in  private  hands,  the  desire  on  the  part  of  the  public 
for  drastic  interference  with  private  rights  will  lose  its  force. 

131.  Forms  for  Specific  Accounts  in  Forestry.  —  The  accounts 
kept  by  the  proprietors  of  a  large  business,  involving  the  owner- 
ship and  management  of  many  separate  parcels  of  forest  land,  and 
a  more  or  less  continuous  annual  income  and  outlay,  must  show 
specifically  the  cash  transactions  and  actual  cost  of  the  property. 

The  capital  accounts  should  record  cost  of  permanent  assets. 
But  to  this  cost  may  be  added  the  annual  excess  of  actual  cash 
expenses  over  annual  income,  incurred  for  the  care  and  mainte- 
nance of  the  property  (§57).  The  only  alternative  is  to  exhibit 
a  corresponding  deficit  in  the  balance  sheet.  The  choice  between 
these  methods  will  be  based  on  the  character  of  the  assets. 
For  property  increasing  in  value  by  natural  growth  of  timber 
there  can  be  no  serious  objection  to  the  process  of  adding  actual 
costs  to  the  capital  account. 

A  depreciation  fund  is  seldom  required  for  such  an  enterprise. 
The  equipment  subject  to  depreciation  is  of  such  small  total 
value  that  it  will  usually  appear  as  expense. 


BALANCE   SHEET 


Assets 

Capital  assets: 
Land. 
Timber. 
Other  property 

less  depreciation. 
Current  assets: 
Cash. 
Accounts  receivable. 


Liabilities  and  Proprietorship 
Capital  paid  in. 
Surplus. 

Loans  (liabilities). 

Current  liabilities: 
Accounts  payable. 


n8 


FOREST  VALUATION 


TRADING,  AND  PROFIT  AND  LOSS  ACCOUNT 
A.  —  LAND 


Debit 

Cost,  to  date  of  sale. 
Balance,  gross  profit,  to  general  outlay 
and  income  account. 

Debit 

Cost,  to  date  of  sale. 
Balance,  gross  profit,  to  general  outlay 
and  income  account. 

C.  —  GENERAL  OUTLAY 

Debit 

Silvicultural  operations. 
Protection. 
Maintenance. 
Administration. 
Taxes. 

Loss,  from  lands. 
Loss,  from  timber  stumpage. 
Balance  (profit). 


Credit 
Sales. 
Balance,  loss,  to  general  outlay  and  in- 


come account. 


B.  —  STUMPAGE 


Credit 


Sales. 

Balance,  loss,  to  general  outlay  and  in- 
come account. 

AND  INCOME  ACCOUNT 
Credit 
Leases. 
Grazing. 

Secondary  forest  products. 
Thinnings. 
Profit,  from  lands. 
Profit,  from  timber  stumpage. 
Balance  (loss). 


Balance  (loss). 

Interest  on  loans. 

Depreciation. 

Surplus  (profit  for  period). 


Balance  (profit). 


Deficit  (loss  for  period). 


CAPITAL  ACCOUNTS 
D.  —  LAND. 


Debit 

Cost,  by  parcels. 

Additions  to  cost  by  reason  of  annual 
cash  expenses. 


Credit 

By  cost  to  date  of  sale. 
Balance. 


E.  —  STUMPAGE. 


Debit 


Cost,  by  parcels. 

Additions  to  cost  by  reason  of  annual 
cash  expenses. 


Credit 

By  cost  to  date  of  sale. 
Balance. 


F.  —  DISTRIBUTION  OF  ANNUAL  Loss,  FROM  PROFIT  AND  Loss  ACCOUNT 


Debit 


Deficit. 


Credit 

By  increase  of  capifel  assets. 


FOREST  STATICS  —  BALANCE   SHEET  —  PROFITS 
G.  —  DISTRIBUTION  OF  SURPLUS 


Debit 


To  dividends. 


Credit 
Surplus,  profit  and  loss  account. 


H.  —  CHANGES  IN  VALUE  OF  CAPITAL  ASSETS 


Debit 

Appreciation  or  marking  up  of  value  of: 
Stumpage. 
Land. 


Credit 
To  appreciation  of  assets. 


Depreciation  of  assets. 


To  losses  of  timber-  by  reason  of  fire, 
etc.,  not  insured. 


132.  Forms  of  Economic  Accounts  in  Forestry.  —  During 
the  formative  or  constructive  period  of  a  forest  investment, 
previous  to  the  receipt  of  the  principal  income,  the  economic 
status  of  the  entire  investment  may  be  shown  by  a  cost  account, 
in  which  accrued  interest  is  charged  against  all  outstanding 
capital  investments. 


Debit 

Outlay  for  all  sources. 
Accrued  interest  on  outlay. 


OUTLAY  AND  INCOME  ACCOUNT 

Credit 

Income  from  all  sources. 
Accrued  interest  on  income. 
Balance,    representing   net   investment 
or  cost. 


Since  such  an  account  is  intended  merely  for  the  owners'  in- 
formation, the  "interest"  cost  is  a  legitimate  one.  In  the  same 
way  the  " economic"  balance  sheet  (§  73)  can  be  made  up  by 
discounting  the  value  of  future  income  and  entering  the  assets 
on  the  basis  of  their  capital  or  expectation  value. 


"ECONOMIC"  BALANCE  SHEET 
Debit 
Expectation  value  of  land  and  young 


Credit 
Total  net  cost  of  land  and  timber  from 

outlay  and  income  account. 
Net    cost    of    improvements    (original 
cost,  less  sums  returned   for  de- 
preciation). 
Potential  surplus. 

It  is  this  balance  which  is  the  object  of  nearly  all  the  calcu- 
lations discussed  under  forest  finance. 


timber. 

Value  of  improvements. 
Potential  deficit. 


CHAPTER   IX 
THE   APPRAISAL    OF   DAMAGES 

133.  Principles  Underlying  Appraisal  of  Damages.  —  In  ap- 
praisals to  determine  damages,  the  principles  underlying  the 
valuation  of  forest  property  reach  their  fullest  development 
and  receive  their  most  complete  application.  When  the  eco- 
nomic basis  of  forest  valuation  is  understood  (Chapter  IV)  it 
will  be  seen  that  the  guiding  principles  of  legal  practice  indicate 
a  consistent  effort  to  apply  this  basis  in  determining  compen- 
sation for  damages. 

The  uncertainty  and  difficulty  of  authoritative  determination 
of  future  values  is  here,  as  elsewhere,  the  most  serious  drawback 
to  the  unqualified  adoption  of  expectation  values  as  the  basis 
for  measuring  losses  or  damages.  Whatever  substitute  methods 
are  adopted,  as,  for  instance,  the  determination  of  cost,  are  dic- 
tated by  the  greater  relative  certainty  of  the  figures  thus  ob- 
tained, which  consideration  may  outweigh  in  importance  the 
fact  that  these  figures  do  not  accurately  represent  actual  value 
or  loss. 

These  legal  principles  may  be  summarized  as  follows: 

a.  Damages    are    payable    in    money.     Compensation,    not 
physical   restoration,   is   required. 

b.  The  difference  in  value  of  the  property  before  and  after 
the  damage  is  the  measure  of  damages.     The  value  of  the  por- 
tion destroyed  is  not  in  itself  the  measure  of  damages,  but  is 
a  means  of  ascertaining  this  difference  in  total  value.     Soil  and 
timber  are  real  estate.    The  value  of  this  real  estate  as  a  whole, 
before  and  after  the  injury,  is  the  measure  of  damages. 

c.  Damages  must  be  appraised  on  the  basis  of  the  most  prof- 
itable use  to  which  a  property  is  adapted,  as  indicated  by  the 
use  of  similar  contiguous  property.     Sale  value  may  or  may  not 
be  a  correct  index  of  real  value. 


THE  APPRAISAL  OF   DAMAGES  121 

d.  Values  must  ordinarily  have  a  commercial  or  utilitarian 
basis,  but  aesthetic  values,  or  the  value  of  "  legitimate  gratifi- 
cation" (§  4),  must  be  recognized  whenever  based  on  elements 
generally  accepted  by  the  public  at  large.     Sentimental  value 
peculiar  to  the  owner  cannot  be  admitted. 

e.  Loss  of  income  may  be  made  the  basis  of  damages;  but 
this  loss  should  be  discounted  to  the  present,  and  will  then  equal 
the  loss  in  capital  value. 

/.  Cost  of  restoration,  while  frequently  ruled  out,  is  admitted 
when  shown  to  be  less  than  value,  or  when  value  is  difficult  to 
determine. 

g.  Ordinary  "profits"  or  income  is  the  basis  of  damages. 
Excessive  profits,  which  do  not  allow  for  normal  losses,  and 
speculative  or  contingent  profits,  which  depend  upon  uncertain 
future  factors,  such  as  increased  prices,  are  not  admitted.  The 
element  of  time,  intervening  between  the  damage  and  the  real- 
ization of  profit,  does  not  bar  the  consideration  of  these  profits 
provided  they  are  reasonably  certain  to  occur  and  are  properly 
discounted. 

h.  Damages  must  be  actual,  present,  imminent  or  reasonably 
certain  to  occur.  The  damage  itself  may  be  indirect,  but  it 
must  be  proximate,  or  traceable  directly  to  the  offending  cause, 
as,  for  instance,  the  destruction  of  crops,  due  to  cattle,  through 
leaving  a  gate  open.  The  physical  destruction  of  property  by 
fire  is  an  actual  present  damage.  The  cause  may  be  a  spark 
from  a  defective  locomotive  igniting  the  debris  upon  an  improp- 
erly cleared  right  of  way,  several  miles  from  the  property 
destroyed.  The  determination  of  the  money  value  of  the  dam- 
age is  the  only  element  of  uncertainty  in  the  process.* 

*  The  entire  subject  of  damages  is  the  source  of  wide  differences  of  legal  opinion 
and  practice  in  different  states.  Precedents  and  rules  adopted  in  one  state  are 
frequently  at  variance  with  the  decisions  in  other  states.  The  measurement  of 
damages  is  largely  a  determination  of  facts  rather  than  of  legal  principles;  the 
ascertaining  of  the  amount  and  character  of  the  injury  done  to  the  property  and 
consequent  income  of  the  plaintiff.  The  above  rules  appear  to  agree  with  the 
principles  laid  down  in  Sedgwick  on  Damages,  Qth  Ed.,  Vol.  3,  §§  931  to  933. 
The  contention  of  foresters  that  expectation  value,  where  it  can  be  determined,  is 
the  basis  of  damages,  finds  its  clearest  legal  expression  in  rule  b  above,  in  which 
form  it  is  receiving  increasing  recognition  in  state  courts.  See  reference  above  for 
citations  of  cases. 


122  FOREST  VALUATION 

134.  Elements  of  Damage  to  Forest  Property.  —  Damage 
may  occur  to  forest  property  through  injury  or  destruction  of 
timber,  soil  or  permanent  and  temporary  improvements.     For 
permanent  improvements,  the  cost  of  replacement  or  repair  is  a 
fair  basis  of  valuation.    For  temporary  improvements,  the  present 
value  would  be  found  by  subtracting  depreciation  from  cost,  or 
estimating  the  future  usefulness  of  the  improvements  destroyed. 
The  problems  discussed  in  this  chapter  are  those  which  deal 
with  damage  to  timber  crops  and  forest  soil. 

The  separate  elements  which  may  constitute  damages  are 
itemized  as  follows: 

Mature  timber. 

Young  or  immature  timber. 

Forest  soil. 

Watershed  protection. 

Reduction  in  total  value  of  property  not  otherwise  damaged. 

Esthetic  values. 

135.  Physical  Separation  of  Timber  from  Soil.  —  Damage 
to  forest  property  may  take  many  forms,  but  only  those  sources 
of  injury  traceable  to  human  agencies  financially  capable  of  mak- 
ing good  the  loss,  are  of  interest  in  appraisal  of  damages.     All 
losses  involving  actual  destruction  of  property  are  irreparable 
in  the  sense  that  the  entire  value  destroyed  is  lost  to  some 
person.     Losses  from  insects,  wind  or  disease  must  be  appraised 
for  the  information  of  the  owner.     But  when  the  loss  is  to  be 
shifted  to  another,  and  collected  by  legal  processes,  its  appraisal 
must  rest  upon  facts  that  can  be  accepted  by  a  jury. 

Timber  trespass  takes  the  form  of  removing  forest  products 
from  the  soil  without  the  consent  of  the  owner  and,  incidentally, 
of  injury  thereby  caused  to  unmerchantable  trees.  The  main 
element  of  damage  is  the  value  of  the  timber  destroyed  or  taken. 

Damage  by  fire  results  in  the  destruction,  or  partial  destruc- 
tion, of  the  tree  growth,  or  merely  in  injury  and  retardation  of 
growth.  Except  in  the  most  unusual  conflagrations,  the  timber 
even  if  completely  killed  is  not  consumed  or  removed  in  the  sense 
that  it  is  in  lumbering.  Much  of  this  fire-killed  timber,  if  large 


THE  APPRAISAL  OF   DAMAGES  123 

enough  to  be  merchantable,  can  be  salvaged.  After  the  great 
fires  of  1910  in  the  Pacific  northwest  about  90  per  cent  of  fire- 
killed  timber  owned  by  private  parties  was  marketed.  If  not 
merchantable,  the  inflammable  dead  material,  rotting  and  fall- 
ing, greatly  increases  the  fire  hazard  (§  200).  In  practically  no 
case  does  fire  bring  about  a  complete  separation  of  the  timber 
from  the  soil. 

136.  Separation  of  Value  of  Timber  from  Value  of  Soil.  — 
As  a  step  in  the  appraisal  of  damages  it  may  be  necessary  to 
determine  separately  the  value  of  timber  and  of  soil. 

By  Formula  G  the  separate  value  of  timber  is 


which  gives  the  value  in  the  year  a  for  the  timber  by  sub- 
tracting the  value  Sv  from  the  total  value  of  the  property. 
The  residual  value,  land,  then  equals  Sv,  and  if  the  damage  just 
equals  the  value  of  the  timber,  it  may  be  appraised  by  this 
means.  But  this  assumes  that  the  physical  separation  actually 
takes  place,  and  that  the  soil  or  property  Sv  is  left,  as  a  result, 
in  the  same  condition  which  it  would  be  in  after  lumbering  and 
brush  disposal.  This  premise  becomes  evident  by  analysis  of 
the  above  formula  which  equals 


. 

i.opn~a      \         i.opn-a/       \         i.op 


I.0pn~a 

In  this  form  the  separate  values  of  land  and  timber  are  clearly 

$ 

shown.     But  the  expression  Sv  —  -  -  —  is  equivalent  to  the 

i  .opn~° 

difference  in  value  of  Sv  if  freed  for  use  now,  and  its  present 
value  if  freed  for  use  only  after  the  lapse  of  n  —  a  years. 
This  difference  is  equal  to  the  present,  discounted  or  capital 
value  of  the  interest  on  Sv  for  n  —  a  years,  or 


124  FOREST  VALUATION 

It  is  important  to  understand  the  significance  of  this  treat- 
ment of  soil  value  in  valuing  timber.  One  way  of  describing 
this  "expense"  is  that  the  owner  of  the  timber  is  charged  with 
the  interest  on  the  soil  value,  or  "soil  rent,"  as  a  cost  of  bringing 
the  timber  crop  to  maturity,  dating  from  the  present  year. 
This  is  the  assumption  made  by  Schlich.*  This  would  class 
soil  rent  as  an  actual  future  cash  expense  similar  to  taxes.  But 
soil  rent  cannot  be  an  actual  future  cost  or  outlay,  unless  a  differ- 
ent person  owns  the  soil  and  rents  it  to  the  one  who  grows  the 
trees.  The  capital  value  of  the  property,  timber  and  soil,  takes 

no  account  of  this  cost  (Formula  D2),  for  v—^-  is  the  dis- 

i.opn  ° 

counted  net  income,  which  constitutes  soil  value. 

A  separation  of  the  present  net  value  of  the  standing  timber 
from  the  value  of  subsequent  crops  (soil  Sv)  gives 

E  =  value  of  timber, 

i.opn~a 

—  =  present  value  of  soil  if  released  in  n  —  a  years. 
i.opn  " 

Comparing  this  with 

F  +  ^jf  E  _  ^  +  ^  =  yalue  of  timber> 
i.opn  ° 

Sv  =  value  of  soil, 

the  sum  of  values  for  soil  and  timber,  or  the  value  of  the  property, 
is  identical,  but  the  proportion  of  this  total  value  assigned  to 
the  timber  is  greater  by  the  first  method  than  by  the  second, 
by  just  the  amount  of  the  discounted  interest  on  Sv. 

In  the  second  method,  instead  of  assuming  that  the  timber 
owner  is  charged  with  interest  on  Sv,  a  much  clearer  conception 
is  that  the  land  owner,  who  in  fact  is  the  same  person,  benefits 
by  the  release  of  his  land  value  from  its  necessary  use  for  n  —  a 
years  to  produce  the  revenue  Y.  He  therefore  cannot,  de- 

Y  4-  E 
mand  the  full  value  -         '  —  E  for  the  crop,  but  accepts  a 

value  smaller  by  the  exact  amount  of  the  excess  in  value  of 

*  Schlich's  "  Manual  of  Forestry,"  4th  Ed.,  Vol.  Ill,  Part  II,  Chapter  III,  p.  133. 


THE  APPRAISAL  OF  DAMAGES  125 

S    over  -  -  --     The  trespasser,  in  settling  the  damages,  thus 
i.opn  a 

"  purchases  "  the  timber  separately  and  is  given  the  benefit  of 
subtracting  the  discounted  future  expense  of  "soil  rent"  in  re- 
duced damages.  It  is  now  possible  for  the  owner  to  obtain 
this  soil  rent  on  another  crop  of  timber  that  can  be  planted 
immediately.  He  is  not  justified  in  collecting  it  in  the  form  of 
increased  net  damages. 

The  subtraction  of  soil  rent  from  present  value  of  standing 
timber  in  appraisal  of  damages  is  therefore  a  mere  matter  of 
book-keeping  between  the  owner  and  the  trespasser,  by  which 
the  owner  is  the  loser  in  damages,  but  is  compensated  by  the 
release  of  the  land. 

It  is  evident  that  unless  these  conditions  are  actually  secured, 
and  the  land  not  only  released  from  the  crop  but  left  in  the  con- 
dition which  would  normally  result  from  logging,  such  an  as- 
sumption absolutely  fails  to  appraise  the  true  damages,  which 
are  in  excess  of  the  amount  indicated. 

In  European  practice,  the  expectation  value  for  the  soil  Sv 
is  first  computed.  This  value  is  then  introduced  not  only  in 
determining  expectation  value  of  standing  timber,  but  is  also 
substituted  for  the  cost  of  the  soil. 

The  effect  of  using  Sv  as  the  so-called  "cost"  of  the  soil  is  to 
eliminate  "profit"  or  enterpriser's  gain,  and  to  balance  costs  and 
income  at  p  per  cent  (§127).  Not  only  will  the  costs  balance 
the  income  at  the  final  year,  but,  by  formula  KI,  substituting 
Sv  for  Se, 

(C  +  Sv  +  E)i  .op*  -  (Sv  +  £)  , 


which  indicates  that  this  so-called  "cost"  is  exactly  equal  to 
expectation  value  of  timber  for  any  year  during  the  growth  of 
the  crop.  This  means  that  if  actual  cost  of  soil  is  not  known, 
or  does  not  enter  into  the  problem,  as  in  the  case  of  govern- 
ment lands,  and  the  returns  from  forestry  are  computed  on  the 
basis  of  a  fixed  rate  of  interest,  p  per  cent,  throwing  all  "profit" 
into  terms  of  soil  value  (§  127),  standing  timber  of  a  given  age 


126  FOREST  VALUATION 

will  have  the  same  value  whether  computed  as  a  cost  or  as  a 
capital  value.  To  compute  this  value  under  actual  conditions 
in  this  country,  either  the  standard  rate  of  interest  for  many 
sections  must  be  very  low  or  a  negative  soil  value  may  have 
to  be  used,  which  is  perfectly  practical.  The  method  is  so 
foreign  to  our  ideas  of  finance  that  it  should  be  discarded  in 
favor  of  the  more  intelligible  plans  of  utilizing  actual  costs  and 
sale  value,  or  of  discarding  altogether  the  subtraction  of  inter- 
est on  soil  as  a  deduction  from  damages. 

137.  A  Basis  of  Damages :  Cost  of  Replacement.  —  The 
objections  to  the  use  of  cost  of  replacement  as  a  measure  of 
damages  are  that  it  does  not  represent  the  true  value  of  the 
property  nor  measure  the  loss  (§§i33&,  68).  Its  merits  lie  in  the 
certainty  of  the  figures,  derived  as  they  are  from  past  experience. 

Very  young  timber  or  reproduction  may  be  completely  de- 
stroyed by  fire.  It  has  no  sale  value,  except,  rarely,  for  Christ- 
mas trees.  The  expectation  value  of  such  young  stands  is 
difficult  to  compute.  But  the  cost  of  planting  and  the  annual 
charge  for  protection  and  administration  can  be  easily  deter- 
mined. 

Assuming  that  the  trees  have  been  completely  killed  and  that 
no  further  expense  is  needed  to  prepare  the  ground  for  a  new 
crop,  the  cost,  including  interest  on  soil,  the  use  of  which  is 
lost,  will  be,  for  a  years, 

(C  +  Sc  +  E)  i.op*  -  (Se  +  E).  (A) 

By  substituting  the  capital  value  of  soil  for  Sc,  this  cost  be- 
comes equal  to  the  expectation  value  of  the  young  timber 
(§  127).  But  this  value  Sv  is  even  more  unreliable  than  the  ex- 
pectation value  of  the  young  stand  (§  116).  If  Se  is  charged 
as  a  cost,  it  will  be  determined  by  the  price  paid  for  the  soil, 
or  the  sale  value  of  similar  bare  land  in  the  vicinity. 

Where,  as  in  government  forests  in  the  west,  land  has  no 
purchase  price,  the  practice  is  to  omit  this  item  from  cost.  The 
cost  of  the  crop  then  becomes 


THE   APPRAISAL  OF   DAMAGES  127 

The  effect  of  this  omission  is  to  decrease  the  damages  demanded. 
The  cost  C  is  included  except  when  natural  reproduction  is 
sure  to  occur.     In  this  case,  C  may  be  omitted,  and  the  damages 
would  then  amount  merely  to  the  annual  expenses 

E(i.opa  -  i). 

In  ordinary  cases,  the  entire  annual  charges,  including  admin- 
istration, taxes  and  upkeep,  would  constitute  the  cost.  But  in 
national  forests,  administration  expenses  are  frequently  offset 
by  revenues  from  grazing,  while  taxes  are  not  paid.  The  item 
e  may  then  include  only  the  cost  of  fire  protection.  The  rate 
of  interest  adopted  in  government  forestry  is  seldom  over  3 
per  cent.  For  these  reasons,  damages  based  on  cost  for  private 
forests  usually  exceed  those  claimed  for  government  timber  of 
the  same  quality. 

Excessive  costs  of  replacement  are  sometimes  demanded  on 
the  basis  that  the  trees  burned  should  be  physically  replaced 
with  others  of  like  size.  An  owner  who  has  a  young  grove 
destroyed  feels  that  the  small  value  represented  by  the  cost  of 
growing  the  trees  does  not  compensate  him  for  the  loss  of  the 
grove.  His  trees  are  gone  and  he  will  have  to  wait  an  equal 
period  for  a  new  plantation  to  attain  like  size.  If  repeatedly 
burned,  he  would  never  secure  his  grove.  The  excess  value 
indicated  in  such  a  case  actually  exists,  both  as  sentiment  on 
the  part  of  the  owner  and  as  an  addition  to  the  value  of  the 
entire  property  (§  1336).  Neither  of  these  elements  are  best 
valued  by  attempting  to  estimate  the  cost  of  immediate  physical 
restoration  of  the  property,  but  are  discussed  under  other  head- 
ings (§§  138  and  147). 

With  increasing  age  of  the  timber,  the  relative  merits  of  cost 
as  a  basis,  compared  with  value,  become  less  and  less.  Wherever 
there  is  a  marked  divergence  in  the  two,  whether  cost  exceeds 
or  is  less  than  value,  the  collection  of  damages  based  on  cost 
cannot  be  justified  by  any  principle  of  law.  Its  use  is  clearly 
a  make-shift  and  will  be  confined  to  young  timber  whose  age 
does  not  exceed  one-half  the  period  required  to  bring  the  trees 
to  maturity. 


128  FOREST  VALUATION 

138.  A  Basis  of  Damages:  Sale  Value.  —  Sale  value  is  a  far 
more  reliable  indication  of  damage  than  cost.  In  forest  property, 
it  is  always  a  question  as  to  whether  the  timber  destroyed  or 
removed  can  be  valued  separately,  and  by  this  means  the  loss 
in  value  to  the  property  as  a  whole  be  determined. 

The  ultimate  sale  value  of  the  timber  is  a  reliable  basis  for 
damages,  as  it  is  the  basis  of  capital  value  not  only  for  the  tim- 
ber but  for  the  soil  as  well  (Chapter  VII).  Whenever  timber 
is  destroyed  which  has  a  present  sale  value,  this  value  must  be 
ascertained,  and  will  be  accepted  as  the  measure  of  damages 
for  the  timber  destroyed,  unless  it  can  be  proved  that  other 
damage  has  been  suffered.  If  the  timber  is  young  and  growing 
rapidly,  or  if  it  is  at  present  inaccessible  but  certain  to  be  de- 
veloped in  the  near  future,  its  present  stumpage  value  or  sale 
value  may  not  represent  its  true  value  to  the  owner,  who  intends 
to  hold  it.  By  proving  with  reasonable  certainty  the  existence 
of  this  higher  value,  sale  value  even  for  merchantable  timber 
can  be  set  aside.  But  the  burden  of  proof  is  on  the  owner,  and 
courts  will  accept  sale  value  for  timber  unless  a  strong  case  for 
higher  values  can  be  shown. 

The  loss  in  sale  value  of  the  entire  property  is  not  so  easily 
gauged.  It  is  a  great  advantage  to  be  able  to  value  the  income, 
in  the  form  of  timber,  rather  than  to  judge  of  the  effect  of  this 
loss  of  timber  upon  the  selling  value  of  the  property.  In  theory, 
the  latter  loss  more  accurately  gauges  the  damage  (§  133^). 
There  are  cases  when  the  value  of  the  materials  destroyed  is 
wholly  inadequate  as  a  measure  of  the  loss  resulting  to  the 
owner. 

The  most  direct  case  is  where  a  portion  of  a  large  stand  is 
destroyed,  appreciably  reducing  the  total  amount  that  may  be 
logged.  This  raises  the  cost  per  thousand  feet,  or  unit,  for 
logging  the  remainder  (§§  98  and  174).  The  increased  cost  is 
subtracted  from  stumpage  value  of  the  remaining  timber.  The 
total  loss  is  equal  to  the  sale  value  of  the  timber  burned  plus 
the  loss  in  sale  value  for  the  entire  remaining  body  of  timber. 

A  woodlot  frequently  adds  materially  to  the  sale  value  of  a 
farm.  Its  destruction  would  represent  a  loss  many  times  greater 


THE  APPRAISAL  OF  DAMAGES  1 29 

than  the  value  of  the  wood,  and,  under  definition  b,  this  difference 
in  value  for  the  entire  property  must  be  the  basis  of  damage. 

For  such  losses,  affecting  the  value  of  the  entire  property, 
the  appraised  loss  in  sale  value  is  the  safest  guide,  as  it  eliminates 
sentiment  or  personal  considerations  (§  i^d). 

Were  the  general  public  fully  alive  to  prospective  values  of 
young  timber  and  of  forest  lands,  and  agreed  upon  the  rate  of 
interest  which  should  apply  to  forest  investments,  and  if  a  suffi- 
cient movement  in  forest  real  estate  existed  so  that  these  opinions 
could  be  crystallized  by  sales,  there  is  no  doubt  that  sale  value 
for  immature  timber  would  approximate  its  real  value  so  closely 
that  it  might  be  accepted  as  a  basis  for  damages  as  readily  as 
the  sale  value  of  mature  or  saleable  trees.  This  would  be  an 
immense  advantage,  as  there  is  never  any  objection  to  accept- 
ing sale  values  whenever  they  are  evidently  just  to  the  owner. 
But  with  the  growing  of  trees  as  a  business  still  in  its  infancy, 
or  perhaps  not  practiced  at  all,  the  sale  value  of  such  young 
timber  is  likely  to  be  far  below  its  capital  or  expectation  value. 
Under  principle  c  (§  133)  a  great  injustice  would  be  done  the 
owner  by  accepting  such  a  basis  of  settlement. 

In  regions  where  immature  timber  is  commonly  regarded  as 
having  little  if  any  value,  the  claimant  must  prove  the  injus- 
tice of  such  valuation  by  demonstrating  his  intention  and  ability 
to  bring  the  young  trees  to  maturity  and  to  realize  the  ultimate 
revenue.  It  would  be  difficult  for  a  lumberman  who  customarily 
abandons  his  lands  to  fire,  to  do  this.  But  the  United  States 
Forest  Service  has  no  trouble  in  proving  the  value  which  it 
places  upon  such  young  growth.  In  regions  where  forestry  is 
extensively  practiced,  and  upon  lands  which  the  owner  has  had 
under  management,  such  as  plantations,  not  only  will  sale  value 
more  nearly  approximate  real  value,  but  it  will  be  easier  to  secure 
the  true  expectation  value  independent  of  the  standard  set  by 
sales. 

139.  A  Basis  of  Damages:  Expectation  or  Capital  Value.  — 
Not  only  does  sale  value  fail  to  establish  the  value  of  property 
to  the  owner  for  his  own  use,  when  this  value  is  unfamiliar  to  the 
public  at  large,  but  it  frequently  happens  that  there  are  no  sales 


130  FOREST  VALUATION 

of  similar  property  on  which  to  base  such  values.  There  is  a 
further  difficulty  in  judging  of  the  loss  in  sale  value  resulting 
from  the  damage.  For  these  reasons,  and  in  order  to  base  the 
damage  fairly  upon  loss  in  income  or  use,  the  capital  value  or 
expectation  value  of  the  property,  as  well  as  of  the  portion  de- 
stroyed or  income  lost,  must  be  calculated,  in  spite  of  its  uncer- 
tainties. These  uncertainties  (§  67)  lie  in  the  determination  of: 

Future  yield  of  merchantable  material. 

Date  of  maturity  or  final  cutting. 

Future  price  of  products. 

Rate  of  interest  adopted. 

Authoritative  studies  of  the  yields  per  acre  for  important 
commercial  species  are  becoming  available  which  indicate  not 
only  the  amount  of  merchantable  material  to  be  expected, 
but  the  proper  age  at  which  to  cut  the  stand.  In  the  absence 
of  such  data,  experience  of  farmers  and  woodlot  owners  in  re- 
gions of  second  growth  can  be  cited. 

It  might  seem  that  the  certainty  of  the  upward  tendency  of 
prices  for  wood  products  would  justify  the  adoption  of  higher 
stumpage  values  as  a  basis  of  damages  for  destruction  of  young 
timber  (Chapter  XII).  This  argument  is  ingeniously  used  by 
the  Forest  Service  to  justify  valuation  of  very  young  timber  on 
the  basis  of  cost  and  thus  secure  higher  values  than  would  be 
shown  by  capitalizing  income  on  the  basis  of  present  stumpage 
prices.  It  is  probably  true  that  owners  forced  to  accept  settle- 
ment on  terms  of  expectation  value  based  on  present  prices, 
for  timber  which  will  not  mature  for  several  decades,  are  losing 
a  profit  which  in  all  reason  they  may  expect.  But  the  deter- 
mination of  the  amount  of  this  increase  introduces  a  speculative 
element  into  a  calculation  already  sufficiently  complicated,  and. 
runs  directly  counter  to  principle  g  (§  133).  Damages  are  in- 
tended to  fully  compensate  the  owner  for  reasonable  profits, 
and  no  objection  can  be  raised  to  admitting  the  effects  of  the 
growth  of  the  timber  or  its  increase  in  quality,  but  the  fluctua- 
tion of  stumpage  prices  will  not  ordinarily  be  admitted  by  a  court 
and  it  is  the  part  of  wisdom  to  base  the  evidence  upon  prevailing 
prices.  In  such  calculations  as  an  owner  may  make  for  his  own 


THE  APPRAISAL  OF   DAMAGES  131 

information,  he  is  at  liberty  to  speculate  on  the  increase  in 
prices  as  he  sees  fit. 

The  rate  of  interest  will  remain  a  matter  of  dispute  until 
forest  production  takes  its  place  as  a  recognized  business.  The 
higher  the  rate  used,  the  smaller  and  more  conservative  will  be 
the  value  placed  upon  the  damage.  This  is  directly  opposite  to 
the  effect  of  a  high  rate  used  in  calculating  cost  of  replacement. 
In  such  a  case,  the  higher  the  interest  rate,  the  greater  will  be 
the  cost,  and  the  smaller  the  value  of  the  crop  (§121). 

140.  Damages  to  Merchantable  Timber.  —  Timber  killed  by 
fire  is  saleable  if  accessibly  located  and  a  market  exists  capa- 
ble of  absorbing  it  before  it  deteriorates  from  rot  and  insects. 
If  sales  can  be  made,  the  damage  is  the  difference  in  value  of 
the  timber  before  and  after  the  fire.  To  this  loss  must  be  added 
the  loss  in  stumpage  value  of  timber  not  burned  but  whose 
logging  costs  are  increased  as  a  result  of  the  diminished  quan- 
tity of  stumpage  (§  138). 

Let  y'  =  value  of  damaged  timber, 

L  =  total  damage. 

The  loss  is  expressed  as 

L  =  Y  -Y'.  (O) 

Timber  cut  illegally  may  be  settled  for  with  or  without  suit, 
on  the  basis  of  the  stumpage  value.*  But  it  is  poor  satisfaction 
to  an  owner  to  collect  merely  the  present  value  for  small  timber 
which  he  desired  to  preserve.  Additional  damages  can  be  ob- 
tained by  the  owner,  if  he  can  prove: 

a.  That  the  expectation  value  of  the  timber  is  greater  than 
its  present  stumpage  value.     Unless  increase  in  prices  is  per- 
mitted, this  is  not  always  easy  to  show. 

b.  That  the  sale  value  of  the  entire  property  has  been  in- 
jured by  the  cutting. 

*  An  important  principle  of  damages  widely  recognized  is  that  in  case  of 
wilful  trespass,  the  value  of  the  products  wherever  found,  is  the  measure  of  the 
damages.  In  such  cases  the  value  of  the  timber  after  felling,  transportation,  or 
manufacture  may  be  the  basis  of  damages.  Sedgwick  on  Damages,  gth  Ed., 
Vol.  Ill,  §  934. 


132  FOREST  VALUATION 

c.  That  its  value  for  other  uses,  as  park  purposes,  has  been 
injured. 

He  may  also  instigate  a  criminal  action  against  the  perpetrator 
provided  the  trespass  is  wilful.  In  case  of  a  logging  contract 
under  which  the  contractor  is  required  to  leave  trees  of  certain 
sizes,  constant  inspection  by  the  owner,  cancellation  of  the 
contract,  or  perhaps  a  clause  requiring  payment  of  double 
value  for  forbidden  timber  is  more  effectual  than  damage 
suits. 

Merchantable  timber  injured  by  fire  but  not  killed  must  be 
appraised  on  the  basis  of  its  present  saleability,  and  the  extent 
and  character  of  the  damage  to  its  sale  value.  If  it  can  be  sold 
at  once,  the  loss  will  be  measured  by  deterioration  in  grade 
and  quantity  due  to  the  fire.  If  it  must  remain  for  some  years, 
a  further  deterioration  may  be  expected  as  the  result  of  fungi 
and  insects.  If  this  can  be  measured,  it  should  be  allowed. 
Timber  whose  sale  is  necessarily  postponed,  even  if  of  mer- 
chantable size,  should  be  valued  by  the  same  method  as  young 
or  immature  timber.  Its  expectation  value,  as  reduced  by  rot 
and  insects,  and  not  its  present  sale  value,  should  be  the  basis 
of  damage. 

141.  Damage  to  Immature  Timber:  Partial  Loss.  —  For 
reasons  given  in  §  138,  sale  value  for  immature  timber  de- 
stroyed does  not  compensate  the  owner,  and  it  rarely  happens 
that  the  sale  value  of  the  property,  either  before  the  damage 
or  after  it  occurs,  is  a  safe  index  of  the  damage.  Cost  of 
replacement  may  be  used,  as  suggested  in  §  137.  But  for 
timber  more  than  half  grown  or  approaching  maturity,  capital 
or  expectation  value  must  be  the  means  of  approximating  the 
loss  in  value  to  the  property,  and  this  method  should  always 
be  used  as  a  check  on  cost,  even  for  very  young  stands. 

Where  a  stand  is  injured  but  not  killed,  the  trees  will  continue 
to  occupy  the  soil  until  they  reach  merchantable  size  and  are 
cut.  The  damage  to  the  crop  is  measured  by  the  loss  in  value 
of  the  timber  when  cut,  traceable  to  the  fire. 

Y  =  original  expected  value  of  timber  when  cut, 
V  =  expected  value  as  reduced  by  fire  damage. 


THE  APPRAISAL  OF  DAMAGES  133 

The  future  net  value  of  each  of  these  crops  in  the  year  n  is, 
respectively,  when  5  represents  either  Sc,  Sv  or  S,, 


F  - 

as  the  expenses  continue  undiminished.    The  difference  in  net 
value,  representing  damages,  is  Y  —  Y'  .     Discounting  this  loss 

Y  _  Y' 

to  the  present  year  a  gives  -  ^-  (Oi) 

Under  normal  conditions,  the  expected  value  of  the  crop  cannot 
exceed 


But  if  F'<(S  +  E)(i.o^-«-i), 

then  7  -  Y'  >  Y  -  (S  +  £)  (i.o^«-  -  i), 

and  damages  will  exceed  the  expectation  value  of  the  timber. 
That  this  result  coincides  with  actual  conditions  can  be  easily 
shown.  A  damaged  crop  of  timber  which  will  just  pay  expenses 
can  be  left  till  mature.  But  what  is  to  be  done  with  a  stand 
damaged  so  severely  that  it  will  not  meet  these  future  expenses? 
Its  presence  prevents  the  use  of  the  land  for  a  new  crop,  yet  the 
cost  of  removing  it  is  a  net  loss.  Assuming  that  the  timber 

Y  —  Y' 

will  be  left  standing,  —        -  should  be  used  whenever  Y'  can 
i.opn  ° 

be  determined.  The  total  loss  to  the  value  of  the  property 
rather  than  to  the  timber  is  thus  measured  (§  1336). 

142.  Damage  to  Immature  Timber:  Total  Loss.  —  When 
immature  timber  is  totally  destroyed  or  so  badly  injured  that  it 
must  be  removed  if  any  further  profitable  use  is  to  be  made  of 
the  soil,  two  factors  influence  the  method  of  appraisal.  The 
soil  is  released  by  this  removal,  and  its  value  advanced  from 

$ 

-  to  Sv  (§  136).     But  the  value  Sv  is  materially  altered 

to  the  injury  of  the  owner.  As  Sv  is  merely  the  value  of  the 
discounted  net  income,  all  future  expenses  directly  diminish 
this  value,  as  is  seen  in  the  formula  for  Sv  or 


134 


FOREST  VALUATION 


The  initial  expense  C  includes  brush  disposal,  soil  prepara- 
tion, and  the  cost  of  securing  reproduction.  The  removal  of 
burned  and  worthless  timber  increases  C  abnormally.  The 

expense    E  representing  -  includes  fire   protection.     A   fire 

trap,  caused  by  debris,  must  either  be  removed  as  an   initial 
cost  or  an  additional  annual  expense  er  be  incurred,  propor- 
tionally increasing  E  to  E'  for  at  least  a  few  years. 
If  the  value  of  the  burned  timber  is  appraised  as 


the  owner  must  be  left  in  possession  of  a  value  for  land,  Sv,  un- 
diminished  by  such  expenses  (§  136).  The  expense  of  restoring 
this  value  is  (C'  +  E'}  -  (C  +  E),  in  which  (C'  +  E'}  repre- 
sent the  costs  of  securing  and  protecting  the  new  crop  after  the 
fire.*  For  instance,  should  natural  reproduction,  by  sprouts  or 
seed,  be  the  normal  method,  but  as  a  result  of  the  fire,  planting 
becomes  necessary,  the  cost  of  planting  constitutes  a  damage. 
If  the  owner  would  have  had  to  plant  anyway,  the  damage  in- 
cludes only  the  cost  of  removing  the  debris  or  protecting  the 
plantation  from  extra  fire  hazard. 

The  damage  where  young  timber  is  totally  destroyed  may  be 
summarized  as: 

Timber  destroyed  =  Y  +  S°  +  E  _  (^  +  £) 

i.opn  ° 

Further  damage  to  property  =  Sv  —  S'v, 

Total  damage  =  Y  +  Sv  +  E  _  ^,  +  £, 

i.opn  ° 

In  other  words,  the  value  of  the  soil  resulting  from  the  fire  can 
be  substituted  for  its  value  previous  to  the  fire,  thus  covering 
the  total  loss  in  value  of  the  entire  property.  But  as  (C'+  E')  - 

*  This  formula  is  technically  incorrect,  since  the  additional  expense  e'  —  e 
endures  probably  for  but  a  limited  period  b.  Hence  the  increased  cost  of  this 
item  is  (£'  —  £)  (i.op*>  —  i)  instead  of  (£'  —  £).  This  alteration  may  be  made 
in  formula  O2. 


THE  APPRAISAL  OF  DAMAGES  135 

(C  +  E]  as  an  expense  is  the  equivalent  of  Sv  —  S'v  in  future 
value,  the  practical  application  of  this  problem  consists  in  es- 
timating the  costs  of  restoring  the  soil  to  its  original  condition, 
Sv,  and  adding  these  future  costs  to  the  value  of  the  timber 
destroyed.  It  must  be  emphasized  that  this  is  not  an  awarding 
of  double  damages  but  that  the  two  items  are  absolutely  distinct 
and  their  sum  represents  the  loss  in  value  of  the  property.  The 
formula  should,  therefore,  be  expressed, 

L  =  F  +  ^  +  £  +  C'  +  £'-  (C  +  E).  (02) 

i.opn 

The  cost  of  removing  dead  timber  and  debris  and  any  extra- 
ordinary cost  of  securing  reproduction  is  thus  seen  to  be  a  legiti- 
mate damage  wholly  apart  from  and  in  addition  to  the  value  of 
the  timber  destroyed. 

143.  Damage  to  Forest  Soil.  —  Damage  to  the  soil  results 
frequently  from  fire,  and  sometimes  this  is  so  serious  that  the 
soil  is  entirely  destroyed.  This  damage  takes  two  forms, 
actual  physical  injury  by  destruction  of  litter,  humus  and 
beneficial  bacteria  with  resulting  impoverishment  of  the  soil, 
and  loss  of  profits  or  net  income  from  either  present  or  future 
crops  of  timber,  without  necessarily  injuring  the  soil  itself.  Both 
results  usually  occur  and  there  is  no  accurate  way  of  measuring 
the  injury  to  the  soil,  in  terms  of  money,  except  through  loss  in 
probable  income  from  timber  crops. 

Damage  to  soil  resulting  in  destruction  of  litter  and  humus, 
but  which  does  not  kill  the  standing  or  growing  trees,  results 
in  retarding  their  growth.  This  decreases  the  volume  and  value 
of  the  crop.  The  damage  is  measured  by  the  reduced  value  of 
the  standing  timber  (§  141,  Oi). 

Damage  to  soil  accompanied  by  complete  destruction  of 
timber  can  be  measured  only  by  the  probable  effect  of  this 
injury  on  the  value  of  a  new  crop  of  trees.  When  the  soil  is 
largely  vegetable,  as  in  swamps  or  on  high  mountain  slopes,  its 
destruction,  especially  on  slopes,  may  prevent  all  further  tree 
growth.  The  damage  then  equals  Sv  in  addition  to  the  value 
of  the  timber  burned.  When  the  soil  is  partially  destroyed, 


136  FOREST  VALUATION 

it  will  be  difficult  to  estimate  accurately  the  probable  loss  on  a 
new  crop,  unless  the  effect  of  similar  burns  can  be  cited. 

The  cost  of  restoring  soil  value  by  removal  of  debris  (§  142, 02) 
is  wholly  apart  from  the  appraisal  of  physical  damage  to  the 
soil  itself.  Except  in  unusual  cases,  this  physical  damage  is 
exceedingly  difficult  to  measure  in  terms  of  value,  and,  where 
timber  is  destroyed,  destruction  of  soil  represents  but  a  small 
proportion  of  the  total  loss.  This  item  of  damage  is,  therefore, 
neglected  in  most  instances. 

144.  Damage  to  Single  Trees.  —  When  the  expectation 
value  of  young  timber  is  made  the  basis  of  damages,  and  the 
present  value  of  future  crops  is  calculated,  the  future  expenses 
deducted  from  value  are  based  on  the  acreage  protected  and 
utilized  by  the  crop.  The  yield  of  the  timber  is  also  computed 
on  the  basis  of  area,  and  in  this  way  the  normal  loss  in  numbers 
which  occurs  in  all  stands  with  increasing  age  is  allowed  for. 

In  scattered  stands  of  timber,  the  individual  tree  becomes 
more  important,  and  this  importance  increases  in  stands  com- 
posed of  trees  of  many  ages.  Damage  or  loss  in  such  forests 
cannot  as  easily  be  appraised  as  for  crops  of  even-aged  trees. 
The  mature  timber  can  be  estimated  according  to  its  merchant- 
able contents.  If  these  trees  are  still  small,  though  merchant- 
able, it  may  be  possible  to  show  that  their  future  increase  in 
volume  and  quality,  with  consequent  increase  in  value,  is  such 
that  this  discounted  value  exceeds  the  present  value  of  the 
trees. 

If  it  be  assumed  that  all  trees  now  merchantable  will  remain 
standing,  and  future  expenses  are  neglected,  the  expectation 
value  so  obtained  will  be  too  high.  Such  figures  must  be  reduced : 

By  allowing  for  loss  of  numbers; 

By  pro-rating  the  crop  expenses  among  the  reduced  stand,  per 
tree,  according  to  present  volume. 

The  immature  portion  of  such  stands  cannot,  with  any  degree 
of  accuracy,  be  valued  on  the  basis  of  individual  trees.  The  loss 
in  numbers  previous  to  maturity  increases  with  decreasing  age, 
and  the  proportional  expense  to  be  charged  to  each  tree  becomes 
wholly  problematical. 


THE  APPRAISAL  OF   DAMAGES  137 

145.  Damage  to  Many-aged  Stands.  —  The  value  of  damage 
to  a  many-aged  stand  is  determined  by  the  character  and  value 
of  the  stand.     Should  the  timber  be  entirely  destroyed,  its  value 
corresponds  to  that  given  in  §117  or  §118,  according  to  the 
age   classes   represented.     The  keynote  in  valuing   damage  to 
stands  containing  both  immature  and  mature  trees  of  different 
ages  on  the  same  area  is  to  attempt  to  separate  the  stand  into 
its  age  classes  according  to  the  area  which  each  really  occupies. 
This  permits  of  the  distribution  of  future  costs  and  avoids 
double  valuation. 

For  instance,  suppressed  and  stunted  reproduction  growing 
under  old  timber  may  be  considered  as  occupying  little  if  any 
area.  But  if  this  reproduction  would  have  been  the  means 
of  forming  a  second  crop  after  logging,  it  must  be  valued.  Its 
age  should  be  taken  not  as  the  actual  age  resulting  from  sup- 
pression, but  as  the  age  of  trees  of  similar  size  grown  in  open 
land.  Means  of  determining  accurately  the  proportional  areas 
occupied  by  age  classes  in  such  forests  are  not  yet  perfected. 
But  an  approximation  of  the  area  and  average  "economic" 
age  of  the  crop,  or  age  of  an  even-aged  stand  of  equal  volume 
and  sizes,  is  the  only  satisfactory  basis  for  arriving  at  damages. 

The  first  step  is  to  decide  upon  the  area  which  should  be 
assigned  to  immature  timber  as  a  whole.  The  remaining  area 
is  that  occupied  by  mature  trees.  The  appraiser  then  decides 
whether  to  divide  this  immature  timber  into  several  age  classes, 
or  to  assume  an  average  age  for  the  entire  crop  and  treat  it  as 
an  even-aged  stand  of  that  age.  If  more  than  one  age  class  is 
required,  the  area  and  average  age  for  each  is  determined.  In 
this  manner  the  even-aged  stand  and  area  become  the  basis  of 
appraisal  of  damages  for  many-aged  forests  (§  140  to  142). 

146.  Damage    to    Watersheds.  —  The    protective    value    of 
forest  cover  affects,  first,  the  soil  itself  and  its  ability  to  produce 
timber  crops,  and  second,  the  property  and  interests  affected 
by  stream  flow. 

Soils  subject  to  erosion  may  be  completely  ruined,  even  for 
tree  growth,  by  the  effect  of  removing  the  timber  cover  through 
fire  or  logging.  This  loss  would  be  measured  as  in  §  143. 


138  FOREST  VALUATION 

But  the  damage  inflicted  on  other  property  caused  by  the  in- 
creasing irregularity  of  stream  flow,  floods  followed  by  almost 
complete  cessation  of  flow,  the  silting  up  of  streams  and  reser- 
voirs, and  the  consequent  damage  to  navigation,  waterpowers, 
irrigation  and  agriculture  are  additional  to  the  loss  of  the  timber 
and  soil  on  the  property  itself.  Deliberate  ruin  or  removal  of 
necessary  timber  cover,  and  destruction  of  grass  and  brush  by 
over-grazing,  probably  renders  the  owner  of  such  lands  liable  for 
the  resulting  damages  to  others.  But  the  connection  between 
cause  and  effect,  while  proved  beyond  a  doubt,  is  very  difficult 
to  express  in  money  value.  Large  areas  of  watershed  contribute 
to  the  result,  and  the  damage  extends  over  many  years  and 
varies  according  to  rainfall  and  other  circumstances.  To  deter- 
mine the  proportion  of  this  ultimate  probable  damage  for  which 
the  denudation  of  one  acre  is  responsible,  is  a  mere  guess.  Such 
protective  areas  should  be  acquired  by  national  or  State  govern- 
ments and  the  damage  prevented,  rather  than  to  attempt  to  force 
private  owners  to  preserve  the  forest  for  the  benefit  of  others, 
or  endeavor  to  collect  damages  from  such  owners  for  the  in- 
juries caused  by  their  abuse  of  the  forest  cover. 

In  the  absence  of  commercial  value,  as  where  forests  are  in- 
accessible and  cannot  be  cut,  the  cost  of  re-establishing  the 
protective  cover,  either  by  natural  or  artificial  means,  and  of 
protecting  this  area  from  fire  until  it  reaches  the  same  state  of 
effectiveness  as  that  which  was  removed,  can  properly  be  con- 
sidered as  a  measure  of  damages.  It  is  also  possible  in  the  case 
of  forest  users,  such  as  lumbermen,  to  set  an  arbitrary  value  per 
acre  for  the  protective  influences  of  the  cover,  and  bind  the  user 
by  private  contract  to  pay  this  sum  in  case  of  fire  occurring 
through  the  carelessness  of  his  employees. 

As  knowledge  of  the  effect  of  forests  on  flow  of  streams  is  ob- 
tained, it  will  become  possible  to  arrive  at  a  value  per  acre  of 
the  protective  influence  of  the  forest  cover  on  different  water- 
sheds. This  value  may  then  be  used  in  damage  suits. 

147.  ^Esthetic  Values.  —  The  fundamental  character  of  the 
value  represented  by  an  appeal  to  the  aesthetic  sense  must  be 
recognized  in  appraising  damages  (§  4).  The  gratifications  for 


THE   APPRAISAL   OF   DAMAGES  139 

which  mankind  will  pay  money  are  by  no  means  confined  to  the 
material  demands  of  the  body.  Simply  because  it  is  difficult 
to  place  a  money  value  upon  such  gratification  is  no  reason 
for  denying  its  existence.  Scenery  and  beauty  are  capitalized 
by  those  who  provide  hotels  and  camps  for  visitors,  and  the 
common  rights  in  scenery,  especially  in  the  enjoyment  of  woods 
and  forests,  clash  repeatedly  with  the  private  property  rights 
of  those  who  own  and  may  wish  to  cut  the  timber,  usually  to 
the  loss  of  the  public,  without  recourse  to  damage  suits.  Such 
rights,  just  as  in  the  case  of  watersheds,  are  best  protected  by 
public  ownership  of  lands  and  forests  which  have  peculiar  or 
exceptional  value. 

But  the  private  owner  who  has  acquired  property  of  scenic 
and  aesthetic  value  is  not  obliged  to  accept  merely  the  commer- 
cial value  of  the  income  from  wood  products  as  full  settlement 
for  damages  caused  by  fire  or  theft.  The  additional  value  is 
as  real  to  him  as  similar  values  are  to  the  public  at  large.  It  is 
just  this  common  or  universal  acceptance  of  this  form  of  value 
which  permits  of  its  appraisal  as  an  element  of  damages.  Pur- 
chasers can  usually  be  found  for  estates  possessing  such  advan- 
tages, and  at  prices  which  would  probably  compensate  the  owner 
for  any  reasonable  cost  he  has  incurred  to  secure  the  results. 
For  this  reason,  the  aesthetic  values  destroyed  may  frequently 
be  gauged  roughly  by  the  loss  in  sale  value  of  the  entire  prop- 
erty. Where  landscape  features  are  affected  the  damage  can 
best  be  appraised  by  experts  familiar  with  landscape  gardening 
rather  than  forestry. 

148.  Punitive  Damages.  —  Damages  in  excess  of  loss  in 
value  are  sometimes  provided  for  by  law  in  case  of  destruction 
of  property  belonging  to  the  state.  This  is  not  justified  by 
any  principle  applicable  to  private  owners,  but  is  rather  an  at- 
tempt to  enforce  punitive  measures  as  a  matter  of  public  edu- 
cation. It  lies  halfway  between  civil  judgments  and  criminal 
penalties,  in  which  the  offender  is  punished  as  a  public  example. 
The  state  of  New  York  has  such  a  law,  providing  a  penalty  of 
$10.00  per  tree  destroyed  on  the  Forest  Preserve.  The  advantage 
of  combining  punitive  measures  with  civil  suits  for  damages  is 


140  FOREST  VALUATION 

extremely  doubtful,  and  in  suits  instituted  by  New  York,  this 
provision,  while  held  as  a  club  over  the  heads  of  the  offending 
parties,  has  not  been  used  as  the  basis  of  determining  the  dam- 
ages. Even  in  private  contracts  it  has  been  found  advisable 
to  secure  compliance  with  contract  terms  by  other  means  than 
the  enforcement  of  punitive  damages  for  unauthorized  acts. 


CHAPTER   X 
FOREST  TAXATION 

149.  Sources  of  Revenue  from  which  to  pay  Taxes.  —  Taxes 
are  levied  to  raise  funds  with  which  to  meet  the  expenses  of  gov- 
ernment.    They  therefore  constitute  an  annual  charge  against 
the  wealth  of  the  community.     In  both  theory  and  practice 
taxes  are  levied  against  persons  instead  of  property,  and  are 
gauged  according  to  ability  to  pay,  and  not  on  the  basis  of 
benefits  received.     But  the  effect  of  taxation  upon  the  value 
of  productive  property  may  best  be  studied  by  regarding  the 
enterprise  as  the  source  of  the  revenue  required  to  pay  the 
taxes.      The  expense  of  taxes  must  be  met  eventually  from 
income,  as  are  all  other  annual  expenses.     Taxes  must  be  paid 
whether  or  not  this  income  from  the  taxed  property  is  forth- 
coming, and  in  the  absence  of  such  revenue,  or  previous  to  its 
receipt,  must  be  met  by  the  investment  of  additional  capital 

(§  131). 

Such  investments  of  capital  add  nothing  to  the  value  of  the 
property,  and  must  eventually  be  recovered  from  income. 
Should  the  taxes  reach  a  proportion  where  the  entire  net  income 
is  absorbed,  the  property  becomes  worthless  to  the  owner  (§  61) 
and  will  be  abandoned,  as  was  the  case  with  much  cut-over 
timberland  in  the  Lake  States  in  the  early  'QO'S  when  owners 
could  see  no  prospect  of  income  sufficient  to  pay  the  annual 
taxes. 

150.  Tax  on  Income.  —  A  tax  on  income  is  the  most  logical 
method  of  preventing  excessive  taxation.     The  relation  between 
the  income  and  the  tax  is  definite  and  the  collection  of  the  tax 
follows  the  receipt  of  income,  thus  relieving  the  owner  of  the 
necessity  of  borrowing  or  making  additional  unprofitable  invest- 
ment of  capital.     The  determination  of  net  income  raises  the 
question  as  to  the  character  of  expenses  to  be  permitted  as  deduc- 

141 


142  FOREST  VALUATION 

tions  from  gross  income.  A  tax  levied  on  gross  income  must  of 
necessity  be  at  a  lower  rate  than  one  levied  on  net  income,  and 
is  more  easily  computed.  But  net  income  is  a  more  scientific 
basis  of  taxation  since  the  net,  after  subtracting  expenses  inci- 
dental to  securing  it,  is  the  only  portion  of  gross  income  which 
becomes  the  property  of  the  owner  available  to  meet  taxes. 

151.  Tax  on  Value  of  Property.  —  Value  of  property  is  de- 
rived from  net  income  (§  64)  and  may  therefore  be  taxed  directly, 
without  injustice,  provided  the  assessed  value  of  the  property 
does  not  exceed  its  expectation  or  capital  value,  and  the  rate 
of  taxation  on  this  capital  value  bears  the  proper  ratio  to  the 
legitimate  tax  on  income. 

This  ratio  is  dependent  on  the  rate  of  interest  used  as  the 
standard  for  determining  the  capital  value  (p  per  cent).  The 
annual  equivalent  of  intermittent  income  may  always  be  found 
(XIII).  The  relation  between  this  annual  income  and  value  is 

,,.  ,  Income 

Value  =  — 

.op 

T  ,    IO° 

=  Income  X • 


The  expression  is  the  ratio  between  a  tax  on  income  and  on 

P 
capital  value.    It  follows  that  a  tax  equal  to  a  per  cent  of  value 

must  take X  a  per  cent  of  income.    A  tax  rate  of  10  mills,  or 

P 
i  per  cent,  when  the  rate  of  interest  is  5  per  cent,  will  require 

—  X  i  per  cent,  or  20  per  cent  of  the  income,  while  a  2o-mill  tax 

absorbs  40  per  cent  of  income.  With  a  rate  of  interest  of  10 
per  cent  the  proportion  of  taxes  to  income  would  in  this  case  be 
respectively  10  per  cent  and  20  per  cent. 

The  amount  of  the  annual  tax  is  the  product  of  the  assessed 
value  and  the  tax  rate.  The  annual  tax,  rather  than  either  the 
rate  or  the  assessed  value  alone,  determines  the  relative  per  cent 
of  income  demanded.  A  low  valuation  permits  a  proportion- 
ally higher  tax  rate,  while  high  tax  rates  may  be  lowered  with 


FOREST  TAXATION  143 

no  corresponding  reduction  of  taxes  by  increasing  the  assessed 
valuation. 

In  practice,  sale  value  is  made  the  basis  of  valuations  for 
assessment  purposes,  and  since  sale  value  may  not  coincide  with 
expectation  value  (§§  17,  59,  69),  this  may  cause  both  assessed 
value  and  taxes  to  depart  widely  from  the  desired  ratio. 

A  tax  on  sale  value  secures  the  desired  ratio  of  net  income 
most  accurately  when  property  is  producing  this  income  annu- 
ally. When  the  income  is  intermittent  and  deferred,  great  dis- 
crepancies and  inequalities  are  almost  certain  to  exist  in  the 
ratio  between  taxes  and  final  income. 

152.  Taxable  Value   of  Property.  —  The   taxable  value  of 
property  is  the  value  determined  from  future  net  income,  or  its 
capital  value  (§  62)  calculated  by  disregarding  the  future  expenses 
represented  by  the  proposed  taxes,  but  deducting  the  discounted 
value  of  all  other  future  expenses.     The  net  income  which  rep- 
resents this  net  value  is  then  divided  between  the  owner  and 
the  taxing  power,  and  the  owner's  final  net  income  is  what  is 
left  after  paying  his  taxes. 

153.  Effect  of  Taxes  on  Property  Values.  —  This  net  taxable 
value  is  merely  the  sum  of  values  belonging  jointly  to  the  owner 
and    the    taxing   power   or   public.     Nominally   the    complete 
ownership  is  vested  in  the  proprietor.     Practically  the  power 
to  take  income  carries  with  it  and  is  a  manifestation  of  the  sov- 
ereign right  of  ownership,  and  on  failure  of  the  owner  to  pay 
taxes  this  right  is  exercised  by  confiscating  the  property.     But 
the  payment  of  the  tax  results  no  less  in  an  actual  transfer  of 
value  from  owner  to  public.     The  residual  value  after  sub- 
tracting the  taxes  from  net  income  is  the  real  value  of  the  prop- 
erty to  the  owner,  who  is  justified  in  considering  it  as  worthless 
when  the  total  net  income  is  absorbed  by  taxation. 

It  might  be  assumed  that  in  absence  of  taxation,  property 
would  be  worth  the  additional  value  represented  by  the  capi- 
talized taxes.  This  is  literally  true  when  property  is  exempted 
from  taxation  and  at  the  same  time  receives  all  the  benefits  of 
governmental  activities.  Just  as  business  expenses  are  expected 
to  result  in  income  greater  than  the  expense,  so  the  benefits  of 


144  FOREST  VALUATION 

a  government  conducted  by  and  for  the  people,  and  respect- 
ing the  rights  of  property,  should,  on  the  whole,  give  a  full 
equivalent  in  service  for  the  taxes  collected.  Whatever  the 
effect  may  be  upon  the  individual  property  owner,  the  entire 
level  of  values  is  raised  and  the  public  or  common  share  in  this 
increase  should  absorb  less  than  the  total  gain. 

Perfect  equality  of  taxation  on  all  forms  of  income  and  capital 
value  would  have  no  visible  effect  upon  relative  values  of  dif- 
ferent forms  of  property.  But  if  the  burden  of  taxes  is  un- 
equally distributed,  either  by  deliberate  intent  as  is  proposed  by 
the  advocates  of  single  tax  on  land,  or  by  exemptions  of  certain 
forms  of  private  property  from  taxation,  or  merely  by  reason 
of  the  imperfect  working  of  the  machinery  for  assessment  and 
collection  of  taxes,  this  balance  is  disturbed.  The  value  of 
property  over-burdened  with  taxation  is  then  confiscated  in 
actual  reality  and  to  just  the  extent  of  the  excess  of  taxes  above 
the  average  level.  This  serves  to  depress  the  sale  value  of  the 
property  and  lower  its  apparent  taxable  value,  resulting  either 
in  diminished  taxes  or  an  increased  tax  rate  which  still  further 
depresses  values.  The  end  of  the  vicious  process  is  physical 
confiscation  of  the  property,  destruction  of  the  private  enterprise 
dependent  on  it,  and  the  cessation  of  public  revenue  from  taxes 
formerly  received.  Meanwhile,  property  bearing  less  than  its 
share  of  taxes  is  automatically  increased  in  value  and  made 
prosperous  at  the  expense  of  the  over-burdened  forms  of  enter- 
prise, but  only  to  a  certain  extent,  for  the  effect  of  the  destruction 
of  any  form  of  industry  is  a  general  lowering  of  the  value  of 
all  forms  of  property  or  of  the  total  wealth  of  the  community. 
Universal  equality  in  taxation  on  the  basis  of  ability  to  pay 
(§  149)  is,  therefore,  the  goal  of  all  genuine  efforts  at  tax  reform. 

154.  The  General  Property  Tax.  —  The  general  property 
tax  is  a  direct  tax  levied  on  the  assessed  value  of  all  forms  of 
tangible  and  intangible  property  on  the  theory  that  equality 
in  taxation  is  thereby  secured.  In  an  agricultural  age  and 
region  results  were  fairly  equitable.  With  increasing  complica- 
tion of  modern  industrial  development,  the  method  has  become 
less  and  less  effectual,  since  it  fails  to  secure  equal  proportions 


FOREST  TAXATION  145 

of  net  income  from  different  forms  of  property  and  industry. 
As  a  means  of  taxing  standing  timber,  it  is  a  conspicuous  failure 
in  this  respect,  as  the  tax  rates  and  the  total  taxes  paid  on 
timber  bear  no  fixed  relation  whatever  to  the  ultimate  value  of 
the  income. 

155.  The    Problem    of   Taxation    for    Timberlands.  —  The 
failure  of  the  general  property  tax  when  applied  to  timberlands 
is  due  to  several  causes.     Imperfect  and  unequal  valuations 
are  more  prevalent  with  this  class  of  property  than  with  other 
forms,  owing  to  the  inherent  difficulty  of  estimating  and  apprais- 
ing standing  timber  and  the  unfamiliarity  of  tax  assessors  with 
this  work.    This  is  not  a  defect  of  the  system,  but  merely  in 
its  application. 

There  are  three  fundamental  difficulties  in  securing  equitable 
taxation  of  timber  under  this  system,  namely: 

The  difficulty  of  distinguishing  capital  from  income  for  pur- 
poses of  taxation. 

The  practice  of  collecting  taxes  in  advance  of  the  receipt  of 
income. 

The  element  of  time  and  the  resulting  problem  of  interest  in 
its  effect  on  the  relation  between  taxes,  income  and  taxable 
value. 

156.  Distinction  Between   Capital   and   Income   in  Timber 
Properly.  —  Regarded  as  a  crop,  artificially  produced,  the  en- 
tire value  of  timber  represents  the  income  earned  by  the  capital 
invested  in  the  soil.     In  the  form  of  an  even-aged  stand,  the 
increasing  value  of  the  crop  is  merely  the  accumulating  income 
which,  when  finally   cut,  exposes  the  soil  capital  once  more 
(§  1 1 6).     In  determining  the  value  of  this  soil  capital,  all  future 
expenses  are  deducted  at  compound  interest.     The  annual  in- 
come equivalent  to  this  final  income  (Formula  XIII)  is  termed 
soil  rent,  and  the  point  of  view  which  regards  soil  alone  as  capi- 
tal, timber  as  income,  and  requires  all  values  to  be  based  on 
compound  interest,  is  termed  the  theory  of  soil  rent. 

In  contrast  to  this  conception,  land  and  timber  together  may 
be  regarded  as  capital.  A  forest  which  has  been  brought  to  a 
condition  of  complete  normality  (§  109)  capable  of  yielding  a 


146  FOREST  VALUATION 

continuous  annual  income  without  diminishing  the  value  of  the 
capital,  has  an  actual  capital  or  property  value  which  includes 
the  entire  value  of  all  standing  timber.  The  annual  net  cash 
income  from  this  forest  represents  interest  on  this  entire  forest 
value,  and  is  termed  forest  rent.  As  this  income  cancels  annual 
expenses,  compound  interest  on  the  forest  as  a  whole  has  no 
chance  to  accumulate.  The  point  of  view  which  regards  the 
forest,  including  timber,  as  capital,  and  does  not  deduct  com- 
pound interest  on  costs  but  treats  the  entire  forest  as  a  business 
capable  of  producing  annual  net  returns,  is  termed  the  theory  of 
forest  rent. 

The  latter  conception  more  nearly  approximates  the  attitude 
of  investors  in  American  forest  property.  Yet  both  the  con- 
ditions and  the  thoughts  of  investors  occupy  a  position  midway 
between  the  extremes  of  soil  rent  and  forest  rent.  Timber  is 
almost  universally  acquired  in  the  form  of  native  or  virgin 
stands,  already  grown,  and  is  purchased  as  capital.  The  entire 
business,  rather  than  the  stand,  or  parcel,  is  the  basis  of  annual 
income,  if  such  income  is  secured.  The  source  of  this  income 
is  largely  the  increase  in  value  of  the  timber,  rather  by  price 
increment  than  through  growth,  and  in  the  realization  of  this 
income  the  capital  itself  is  liquidated  (§  132).  The  operation 
thus  resembles  a  speculation  similar  to  the  holding  of  unim- 
proved real  estate,  rather  than  a  productive  business  as  contem- 
plated by  the  idea  of  forest  rent.  Under  such  conditions,  the 
distinction  between  capital  and  income  cannot  be  co-ordinated 
with  the  physical  distinction  between  wood  and  soil,  or  between 
wood  capital  and  wood  increment.  It  is  a  mere  matter  of  book- 
keeping based  on  cash  investments  and  cash  returns. 

157.  The  Problem  of  Interest  in  Forest  Taxation.  —  But  the 
problem  of  interest  appears  in  such  investments  in  the  form 
presented  by  the  distinction  between  the  theories  of  soil  rent 
and  forest  rent  (§35).  When  the  investment  as  a  whole  pro- 
duces no  annual  income  for  a  period  of  years,  unearned  interest 
on  the  annual  expenses  accumulates  and  this  time  element  affects 
both  final  "cost"  and  capital  value  of  the  property. 

The  capital  value  of  a  forest  which  will  produce  a  sustained 


FOREST  TAXATION  147 

income  which  is  realized  at  intervals  greater  than  one  year,  may 
be  less  or  greater  than  that  of  a  forest  producing  income  of  the 
same  total  value,  but  in  annual  installments.  The  difference 
in  value  is  due  to  the  same  factors  which  cause  the  difference 
between  soil  value  and  forest  value,  i.e.,  the  income  is  discounted 
by  compound  interest,  and  the  discounted  total  of  future  or 
intervening  annual  expenses  is  deducted  from  value. 

As  touching  taxation  the  question  assumes  this  form:  Shall 
taxes  be  levied  on  actual  present  value  of  property,  or  shall 
deductions  from  this  value  be  permitted,  including  interest  on 
past  costs,  in  arriving  at  the  net  taxable  value?  And  shall 
taxes  paid  in  advance  of  income  be  computed  as  if  drawing 
compound  interest  in  calculating  the  per  cent  of  final  income 
which  such  advance  payments  of  taxes  absorb? 

158.  Effect  of  Present  Condition  of  Forest  upon  Choice  of 
Methods  of  Taxation.  —  These  problems  are  best  presented  by 
a  concrete  example  in  which  the  effects  of  the  two  opposing 
theories  are  illustrated. 

A  stand  of  Loblolly  Pine  in  Maryland  *  yields  products 
worth  on  the  stump: 

At  20  years  of  age $17.81  per  acre. 

At  30  years  of  age 61.14  per  acre. 

At  40  years  of  age 108.91  per  acre. 

At  50  years  of  age 168.49  Per  acre- 

Land  costs  $5.00  per  acre.  Annual  expenses,  exclusive  of  taxes, 
are  3  cents  per  acre.  The  cost  of  securing  reproduction  is  placed 
at  $5.00  per  acre. 

An  interest  rate  of  5  per  cent  will  be  assumed  for  the  problem. 

A  tax  rate  of  20  mills  on  full  value  will  be  assumed.  This 
is  nearly  twice  as  heavy  as  the  average  rate,  yet  it  is  exceeded 
in  many  forest  regions,  especially  in  new  and  poorly  developed 
localities. 

The  area  of  the  forest  will  be  taken  as  50  acres,  and  the  total 
yield  in  50  years  will  be  50  X  $168.49  or  $8424.50.  Three 
cases  are  assumed.  Case  A  is  for  an  even-aged  stand  cover- 

*  Bulletin  n,  U.  S.  Dept.  of  Agriculture,  Jan.  23,  1914,  Table  15,  page  19. 


148 


FOREST  VALUATION 


ing  the  entire  area,  and  cut  at  the  end  of  50  years,  thus  giving 
the  conditions  described  under  soil  rent.  Case  C  is  for  a  stand 
of  all  ages.  There  are  here  50  age  classes,  each  occupying  one 
acre.  The  yield  on  one  acre  is  cut  each  year  perpetually. 
This  crop  may  either  occupy  a  separate  area  as  an  even-aged 
stand  of  one  acre,  or  be  scattered  as  single  trees  throughout  the 
forest.  The  results  will  be  identical.  Case  B  is  for  a  forest 
giving  an  intermittent  yield  every  10  years,  thus  presenting 
five  age  classes  of  10  acres  each. 

Except  for  this  difference  in  the  arrangement  and  present 
condition  of  the  age  classes  of  timber,  the  financial  results  for 
these  forests  are  assumed  to  be  identical.  The  capital  value 
(expectation  value)  of  each  forest  can  be  computed  as  a  basis 
for  taxation. 

Table  II  presents  the  relation  between  a  tax  of  2  per  cent  on 
capital  value  and  an  equivalent  tax  on  income  from  sale  of  timber 
in  each  case. 

TABLE    II 

COMPARISON  OF  RESULTS  FROM  TAXATION  OF  CAPITAL  VALUE  OF  FOREST  SOIL 
AND  OF  SOIL  AND  TIMBER  ON  A  FOREST  OF  50  ACRES 


Basis  of  taxation. 

Character  of 
forest. 

Cutting 
area. 

Period  be- 
tween 
cuts. 

Value  of  yield 
for  period. 

Cash  expenses 
for  period. 

Total 
for 

Per 

Total. 

Per 

period. 

acre.* 

Acres. 

Years. 

A  
B  

Forest  soil. 
Soil  and  timber. 

Even-aged. 
5  age  classes. 

50 

10 

50 

10 

$8424  .  50 
1684.90 

$168.49 
168.49 

$325.00 
65.00 

$6.50 
6.50 

C  

Soil  and  timber. 

All-aged. 

i 

168.49 

168.49 

6.50 

6.50 

*  The  cash  expenses,  85.00  per  acre  for  planting,  and  $1.50  per  year,  or  $.03  X  50  for  protection 
af  the  entire  tract,  are  charged  against  the  area  cut  over  within  the  period. 


Receipts  less 
expenses. 

Cash  expenses 
compounded  to 
year  of  cutting 
at  5  per  cent. 

Net  value  of 
stum  page. 

Capita 
of  prc 

after  r 
ofy 

1  value 
perty 
;moval 
eld. 

Annual  taxes 
at  20  mills 
on  capital 
value. 

Total. 

Per 
acre. 

Total. 

Per 
acre. 

Total. 

Per 
acre. 

Total. 

Per 
acre. 

Total. 

Per 
acre. 

A  
B  
C  

$8099.50 
1619.90 
161.99 

$161.99 
161  99 
161.99 

$3180.87 
100.31 
6.50 

$63.61 
10.03 
6.50 

$5243.63 
1584.59 
161.99 

$104.86 
158.46 
161.99 

$  500.95 
2519.62 
3239.80 

$10.02 
50.39 
64.79 

$10.02 
50.39 
64.79 

$    .20 

I.  CO 

1.29 

FOREST  TAXATION 

TABLE   II.  —  (Continued) 


149 


Total  cash  taxes 
for  50  years. 

Taxes  compounded 
to  year  of  cutting 
at  5  per  cent  . 

Compound  interest 
on  taxes. 

Difference  in  taxes 
and  interest  paid 
on  forests  A  and  B, 
compared  with  C.* 

On  total 
area. 

Per  acre. 

Total. 

Per  acre. 

Total. 

Per  acre. 

Total. 

Per  acre. 

A  
B  
C  
A'  

$  500.95 
2519  62 
3239.80 
2178.50 

$10.02 
50.39 
64.79 
43-57 

$2097.46 
3169.00 
3239.80 
4326.50 

$41.95 
63.38 
64.79 
86.53 

$1596.51 
649.38 

$31.93 
12.99 

$1142.34 
70.50 

$22.84 
1.41 

2148.00 

42.96 

(A'.    Taxes  levied  on  sale  value,  revalued  at  20  years  and  every  10  years  thereafter.) 
*  This  saving  is  largely  due  to  the  fact  that  the  capital  values  of  forests  A  and  B  are  com- 
puted for  the  year  in  which  these  values  are  lowest,  and  remain  at  this  valuation  for  fifty  years. 
See|i6i. 

Per  Cent  of  Values  Taken  by  Taxation,  Computing  Taxes  with  Compound 
Interest  to  Year  of  Final  Yield 


Full  stumpage 
value. 

Net  cash  profit 
on  stumpage. 

Net  value  of 
stumpage. 

A. 

Per  cent 

Per  cent 

Per  cent 

B  
C  
A'  

37.6 
38.4 
Si  3 

39  o 
40.0 

53-4 

40 
40 
82.5 

In  the  problem  discussed,  the  tax  rate  of  2  per  cent  on  full 
value  is  nearly  twice  the  average  rate  of  taxation  on  present 
values  of  forest  property.  But  the  crop  of  timber  chosen  as 
the  basis  of  the  problem  is  more  profitable  than  that  produced 
by  most  species  and  localities.  The  coincidence  between  total 
cash  taxes  for  50  years  at  2  per  cent  and  capital  value  would 
hold  good  only  for  the  same  period  and  rate,  since  2  per  cent  X 
50  =  100  per  cent  of  value. 

159.  Scientific  Taxation:  Forest  Property  Tax.  —  The  value 
given  for  the  forest  in  case  C  is  found  by  deducting  the  annual 
cash  expenses,  $5.00  for  planting  and  3  cents  X  50  acres  or 
$1.50  for  protection.  This  gives  $161.99  as  the  "net"  value 
of  the  annual  crop,  which,  capitalized  at  5  per  cent,  equals 
$3239.50.  (Formula  XII.) 

The  tax,  2  per  cent,  yields  $64.79  annually.  This  is  just 
40  per  cent  of  "net"  stumpage  value  and  a  slightly  smaller 
per  cent  of  sale  value.  The  annual  profit  or  net  income  of 


150  FOREST  VALUATION 

the  forest  coincides  with  net  value  of  the  yield,  and  the  tax,  there- 
fore, takes  40  per  cent  of  this  profit. 

Since  no  one  would  dispute  the  desirability  of  subtracting  these 
current  cash  expenses  previous  to  taxing  stumpage  value,  it  is 
evident  that  for  forests  producing  an  annual  income,  the  tax  on 
forest  capital  and  on  forest  products  are  equal  in  value  and  inter- 
changeable. 

160.  Scientific  Taxation:  Forest  Land  Tax.  —  The  value 
given  for  forest  soil  in  case  A  is  found  by  discounting  the  value 
of  the  final  crop  for  50  years,  treating  it  as  a  recurring  income, 
and  subtracting  the  discounted  cost  of  planting  and  annual 
expenses  in  the  same  manner  (§  116).  This  gives  $500.95  as  the 
capital  value  of  the  soil  just  after  removal  of  the  crop. 

The  tax  of  2  per  cent  on  this  value  for  50  years  amounts, 
in  cash,  to  but  $10.02  per  acre,  as  against  a  cash  total  of 
$64.79  pa-id  by  forest  C.  A  study  of  the  table  explains  this 
discrepancy.  The  sum  of  $31.93  represents  compound  interest 
on  these  taxes  during  the  50-year  period.  The  further  sum  of 
$22.84  represents  a  saving  due  to  the  fact  that  the  capital  value 
adopted  as  a  permanent  basis  for  taxation  is  determined  just 
subsequent  to  the  removal  of  the  periodic  cut  of  timber.  This 
requires  that  the  future  costs  for  planting  and  protection,  amount- 
ing with  interest  to  $63.61,  be  deducted  from  stumpage  value 
previous  to  discounting  (§  105)  to  obtain  capital  value. 

As  a  result  of  this  latter  deduction  or  allowance,  the  total 
taxes  with  interest,  paid  on  forest  A,  amount  to  but  25.9  per 
cent  of  the  stumpage  value  minus  cash  expenses,  or  24.5  per  cent 
of  sale  value.  The  ratio  of  40  per  cent  applies  only  to  the 
reduced  value  or  net  profit  on  the  investment  in  land. 

Forest  B  presents  conditions  midway  between  these  two 
extremes.  The  capital  value  is  found  by  discounting  the  de- 
cennial yield  and  deducting  the  discounted  lo-year  accumulation 
of  expenses,  giving  a  value  of  $2519.62  (§117,  FI).  Upon  this 
value  a  2  per  cent  tax  gives  a  total  cash  payment  of  $50.39 
per  acre  during  the  5o-year  period,  which  is  increased  by  com- 
pound interest  to  $63.38,  leaving  a  small  margin  of  $1.41  as  a 
saving  due  to  the  factors  explained  for  forest  A. 


FOREST  TAXATION  151 

In  computing  the  comparative  per  cents  of  stumpage  value 
taken  by  a  2  per  cent  tax  on  capital  value,  compound  interest 
has  in  each  case  been  added  to  the  taxes,  although  this  item  does 
not  constitute  a  cash  outlay.  It  represents,  rather,  the  equiva- 
lent to  the  community  of  receiving  taxes  in  advance  of  income, 
or  may  be  considered  as  the  discounted  value  of  a  40  per  cent 
income  tax  paid  in  annual  installments  throughout  the  growth 
of  the  crop  instead  of  at  the  close  of  the  period. 

161.  Comparison  of  Taxes  on  Forest  Rent  versus  Soil  Rent.  — 
The  point  at  issue  between  these  two  systems,  both  based  on 
the  taxation  of  capital  value,  is  evidently  the  double  deduction 
from  income,  first,  of  the  future  costs  of  production  with  in- 
terest, exclusive  of  soil,  and  second,  of  the  interest  on  taxes 
paid  previous  to  receipt  of  income.  A  forest  created  by  plant- 
ing or  human  effort  passes  through  stage  A  before  it  can  be 
brought  to  condition  C.  Shall  it,  at  the  latter  date,  be  taxed 
as  for  C  or  continue  to  pay  the  reduced  taxes  computed  for  A? 

This  problem  depends  for  its  answer  upon  whether  future 
conditions,  or  past  conditions,  are  permitted  to  determine  the 
burden  of  taxation.  Both  cases,  A  and  C,  as  well  as  case  B, 
represent  actual  present  value,  based  on  future  conditions. 
When  forest  A  is  brought  into  condition  C,  its  present  value 
is  no  longer  A  but  C  and,  based  on  value,  it  would  pay  the 
taxes  demanded  of  C. 

Taxes  are  based  upon  value  and  not  upon  cost.  Future 
costs  diminish  value  (§  64)  but  past  costs  are  disregarded  in  com- 
puting value  and  do  not  directly  affect  it  (§  68).  By  this  reason- 
ing, the  increasing  tax  which  would  accompany  increased  capital 
value  is  apparently  justified  (§  165).  But  just  as  property  may 
have  a  definite  value  and  still  represent  a  net  loss  to  the  owner 
(§  68),  it  may  be  shown  that  an  owner  of  timberland  cannot  afford 
to  pay  taxes  continuously  for  50  years  and  then  have  these 
back  taxes  completely  ignored  and  be  taxed  on  the  full  value 
of  his  crop.  The  public,  basing  the  tax  on  present  value,  may 
ignore  past  taxes,  but  the  owner,  looking  ahead,  is  not  so  apt  to 
overlook  this  future  possibility.  This  situation  can  only  be 
met  by  a  contract  or  tax  agreement  by  which  the  public  consents 


152  FOREST  VALUATION 

to  forego  taxing  the  full  final  value  C  and  confines  its  tax  to 
present  value  A,  in  return  for  which  concession  the  owner 
agreed  to  undertake  the  growing  of  the  crop.  Past  errors  in 
taxation  will  ordinarily  have  to  stand. 

162.  Scientific  Taxation :  Income  or  Products  Tax.  —  The  tax 
on  income,  correctly  applied,  is  the  mathematical  equivalent 
of  the  tax  on  capital,  provided  the  controlling  rate  of  interest 
can  be  agreed  upon.  But  the  same  difficulty  is  encountered 
in  computing  this  tax  as  was  detected  in  comparing  taxes  on 
forests  A  and  C.  Table  II  shows  income  taxes  purporting  to 
represent  the  equivalent  of  2  per  cent  on  capital  value,  yet  vary- 
ing from  24.5  per  cent  to  38.4  per  cent  of  the  gross  income. 

Net  cash  income  from  either  form  of  forest,  A,  B  or  C,  is  the 
same,  provided  interest  on  expenses  is  neglected,  and  totals 
$161.99  per  acre.  The  "net"  income  corresponding  to  the  capi- 
tal value  is  diminished  in  cases  A  and  B  by  deductions  for 
interest,  which  accounts  for  these  discrepancies.  The  question 
is,  will  such  deductions  be  permitted  in  levying  an  income  tax 
on  present  incomes? 

This  question  is  open  to  the  same  solution  as  that  proposed 
for  the  taxation  of  capital  values.  If  the  income  tax  is  to  be 
substituted  for  an  annual  capital  tax  on  standing  timber,  the 
full  rate  can  be  levied  without  injustice.  But  if  the  income  is 
not  available  until  a  distant  future  period  on  crops  still  immature, 
the  lesser  rate  should  be  promised  and  contracted  for  as  a  future 
system  of  taxation  binding  on  both  parties.  Future  expenses 
must  be  considered  in  a  scheme  of  taxation.  Past  accumula- 
tions of  interest  "cost"  may  be  successfully  ignored. 

This  view  is  confirmed  by  the  attitude  of  the  U.  S.  Collector 
of  Internal  Revenue  in  interpreting  the  income  tax  on  corpo- 
rations dealing  in  timberlands.*  The  ruling  reads:  "In  cases 
where  lands  are  purchased  for  cash,  the  cost  being  the  proceeds 
of  the  sale  of  the  capital  stock  of  the  company,  the  earning 
value  of  the  money  invested,  that  is,  the  interest  which  might 
have  been  received  on  this  money  had  it  been  otherwise  employed, 
cannot  be  added  to  the  initial  cost  of  the  land  to  represent  its 

*  Letter,  Jan.  6,  1914,  to  P.  S.  Ridsdale,  Sec.  American  Forestry  Association. 


FOREST  TAXATION  153 

aggregate  cost  at  time  of  sale.  The  compensation  for  such 
investment  is  the  anticipated  dividends  which  will  be  paid  to 
the  stockholders  out  of  the  profits  when  the  lands  are  sold.  The 
addition  of  the  earning  power  of  the  money  invested  to  the  orig- 
inal cost  of  the  lands  would  operate  as  a  deduction  of  the  divi- 
dend from  gross  income.  Dividends  are  not  deductible,  either 
directly  or  indirectly.  Interest  purported  to  accrue  on  invest- 
ments of  this  character,  made  by  stockholders,  cannot  be  added 
to  the  initial  cost  of  the  assets  for  the  purpose  of  fixing  a  cost 
price  as  the  basis  for  determining  the  profits  accruing  to  the 
corporation  when  such  assets  are  sold." 

Since  these  regulations  state  previously  that  "the  cost  of 
assets  (land  and  timber)  for  the  purpose  of  determining  the 
amount  of  income  resulting  from  a  sale  is  held  to  mean  the  pur- 
chase price  of  the  lands  plus  the  taxes  and  other  carrying  charges 
paid  thereon  prior  to  the  sale,"  it  is  clearly  the  position  of  the 
government  that  interest  on  such  carrying  charges  will  not  be 
permitted  as  a  deduction  from  income.  The  national  income  tax 
on  timberlands  would,  therefore,  be  based  upon  the  theory  of 
forest  rent,  ignoring  interest,  in  spite  of  the  fact  that  this  income 
is  deferred  until  some  future  year  as  in  case  A,  and  not  earned 
annually  as  in  case  C. 

The  tax  would  thus  take  the  same  per  cent  of  income,  whether 
this  income  were  received  in  six  months  or  sixty  years.  For  a 
speculative  business,  where  profits  are  not  dependent  on  a  definite 
period  of  time,  this  method  of  taxing  income  may  not  act  as  a 
deterrent.  But  with  the  production  of  forest  crops,  the  announce- 
ment in  advance  that  "no  deductions  from  the  income  tax  will 
be  permitted  for  interest  on  future  costs  incurred  in  advance 
of  income,"  would  have  a  direct  influence  on  future  profits  and 
act  to  prevent  the  undertaking. 

The  controversy  as  to  whether  interest  is  a  cost  or  an  income 
as  affecting  taxation  either  of  income  or  capital  values  cannot 
be  settled,  but  may  be  dismissed,  with  this  summary;  past 
interest  accrued  on  the  capital  invested  by  the  proprietor  or 
owner  is  not  an  actual  cost,  but  merely  a  method  of  gauging 
profits  and  will  usually  be  neglected  in  taxation.  But  future 


154  FOREST  VALUATION 

interest,  in  the  form  of  discount,  cannot  be  neglected  for  it 
vitally  affects  present  values,  which  are  the  basis  of  present 
taxation.  Whether  or  not  an  income  tax  to  be  collected  at  a 
future  period  shall  be  reduced  on  account  of  deductions  from 
income  of  interest  on  costs,  depends  upon  the  desirability  of 
encouraging  industry  by  granting  this  absolutely  just  conces- 
sion in  advance. 

163.  Scientific  Taxation:  Combined  Capital  Tax  and  Income 
Tax.  —  The  two  systems  of  taxation,  capital  tax  and  income 
tax,  are  thus  seen  to  be  interchangeable  for  property  producing 
annual  income  (C),  but  to  give  widely  divergent  results  for 
property  whose  income  is  intermittent  (A}.  In  the  latter 
case,  either  system  is  open  to  grave  objections.  The  capital 
tax  can  properly  be  computed  only  for  the  year  following  the 
yield,  when  it  is  most  difficult  to  determine  it  exactly  (§  116). 
The  income  tax  wholly  fails  to  satisfy  the  need  for  current 
revenue  for  which  taxes  are  levied.  The  third  difficulty  is  that 
during  the  growth  of  the  timber  and  in  absence  of  definite  pro- 
vision to  the  contrary,  the  constant  tendency  will  be  to  levy 
the  capital  tax  upon  the  existing  value  of  capital  including  the 
timber  as  if  this  temporary  capital  value  were  permanent  and 
capable  of  producing  permanent  annual  income  (§  156). 

In  order  to  secure  regular  annual  revenue  from  taxation 
in  the  absence  of  regular  income  from  lumbering  or  cutting, 
and  at  the  same  time  convince  the  public  that  owners  of  timber 
property  are  paying  their  full  share  of  taxes,  it  is  theoretically 
possible  to  assess  the  capital  value  of  the  property  at  a  portion 
of  its  value  and  postpone  the  collection  of  the  remainder  as  an 
income  tax. 

In  case  A,  the  soil  has  a  capital  value  of  $10.02,  but  can  be 
purchased  at  $5.00  per  acre.*  A  tax  on  $5.00  at  2  per  cent 
will  amount  in  50  years  to  $20.93,  leaving  $21.04  available  as  a 
tax  on  stumpage  at  time  of  cutting.  This  amounts  in  each  case 
to  12.5  per  cent  of  the  "gross"  value,  or  20  per  cent  of  the 
"net"  value  of  the  yield. 

*  This  discrepancy  in  values  is  possible  in  regions  where  the  value  of  land  for 
forest  production  is  not  fully  appreciated. 


FOREST  TAXATION  155 

The  true  equivalents  between  capital  tax  and  income  tax, 
and  the  ratio  of  division  between  them,  depend  first  upon  the 
proportion  of  capital  value  which  is  taxed,  second,  upon  the 
rate  of  taxation  applied  to  it,  and  third,  upon  whether  the  com- 
munity is  willing  in  the  future  to  abide  by  its  agreement  and 
permit  the  owner  to  continue  to  pay  taxes  on  the  basis  of 
capital  values  which  no  longer  represent  the  present  value  of 
the  property.  If  the  rate  is  full,  the  only  margin  left  for  an 
income  tax  is  due  to  a  low  valuation  of  the  land.  If  the  land  is 
valued  at  its  full  capital  value,,  only  a  reduced  rate  will  leave 
a  margin  for  income  tax  on  stumpage.  And  in  case  the  full 
rate  is  collected  for  the  full  period  on  its  original  capital  value, 
the  public  is  entitled  to  an  additional  income  tax  only  by  re- 
pudiating the  owner's  claim  to  deduction  of  interest  on  costs 
from  gross  stumpage  value.  In  practice,  capital  values  of  land 
tend  to  advance  and  the  stumpage  tax  might  well  be  levied  on 
the  increased  value  of  timber  which  is  the  cause  of  this  advance 
in  land  value. 

In  European  systems  of  taxation  both  capital  tax  and  income 
tax  are  usually  levied,  but  the  scientific  relation  between  them 
is  not  determined.  Each  tax  is  assessed  independently,  but 
the  combined  taxes  are  sufficiently  low  so  that  the  property  is 
not  over-taxed. 

164.  Taxes  under  the  General  Property  Tax.  —  Under  the 
general  property  tax,  the  principle  of  taxing  capital  value,  theo- 
retically the  basis  of  the  tax,  is  actually  entirely  superseded 
by  the  plan  of  taxing  sale  value  regardless  of  income.  While 
standing  timber  may  be  legitimately  taxed  as  capital  when, 
as  in  case  C,  only  the  annual  growth  is  removed,  the  effect  of 
annually  taxing  the  sale  value  of  even-aged  crops  is  entirely 
different.  The  distinction  between  capital  and  income  cannot 
be  drawn  with  any  accuracy.  Case  A  presupposes  that  the 
entire  timber  value  represents  income  only  and  not  capi- 
tal. 

The  injustice  in  the  system  consists  in  taxing  annually,  on 
its  full  capital  value,  a  property  which  is  not  producing  annual 
income,  and  which  is  being  held  and  increased  in  value  by  a 


156 


FOREST  VALUATION 


process  similar  to  that  of  savings.*  It  is  as  if  the  owner  of 
property  capable  of  yielding  a  definite  annual  income  of  $168.49 
(Table  II)  allows  this  income  to  accumulate,  although  by  so 
doing  the  earning  power  of  the  property  is  not  increased.  The 
tax  assessor  promptly  adds  this  increment  to  the  assessed  value 
of  the  property,  whereupon  the  owner,  if  he  can,  as  promptly 
withdraws  the  surplus  to  escape  this  excessive  tax.  By  inspec- 
tion of  Table  II  it  will  be  noted  that  the  value  of  the  yield  just 
previous  to  cutting,  for  an  even-aged  forest,  is  $8424.50,  which 
would  be  the  "full"  assessed  value  of  the  property  at  that  time. 
After  cutting,  the  assessed  value  should  not  exceed  $500.95, 
and  in  practice  will  be  nearer  $250.00  if  land  sells  for  $5.00 
per  acre.  The  average  value  for  the  whole  period  would  corre- 
spond closely  to  $3239.80. 

The  tax  assessor,  under  the  present  plan,  bases  his  increases 
upon  market  or  sale  value,  and  as  the  value  of  young  timber  is 
seldom  recognized,  this  sale  value  usually  equals  the  value  of 
the  soil  for  other  purposes,  plus  the  market  value  of  the  timber. 
In  this  way  the  property  escapes  the  full  effect  of  repeated 
taxation  of  capital  value. 

A  comparison  of  values  for  the  crop  used  in  Table  II  gives 
the  following  results. 

TABLE   III 

COMPARISON  OF  SALE  VALUE  WITH  EXPECTATION  VALUE  OF  AN  EVEN- 
AGED  STAND,  INCLUDING  BOTH  LAND  AND  TIMBER 


Age,  years. 

Sale  value  with 
land  at  $5.00. 

Expectation  value 
with  land  at  $10.02. 

10 

$S-oo 

824.83 

20 

22.81 

40.83 

3° 

66.14 

66.90 

40 

113.91                       109.36 

5°                      173-49                         178.51 

The  expectation  value  is  based  in  each  instance  on  the  value 
of  the  crop  at  50  years  (Formula  GI),  and  on  an  interest  rate  of 

*  The  Economic  Problem  of  Forest  Taxation,  by  Fred  Rogers  Fairchild,  Yale 
Review,  February,  1909.  See  also  "  The  Nature  of  Capital  and  Income,"  by  Irving 
Fisher,  pp.  249-255. 


FOREST  TAXATION  157 

5  per  cent.  Basing  the  taxes  on  sale  value  and  revaluing  every 
10  years,  the  total  cash  taxes  paid  during  the  5o-year  period 
amount  to  $43.57  per  acre,  which  is  slightly  less  than  the  amount 
paid  on  forests  B  or  C  for  the  same  period  and  over  four  times 
as  large  as  the  sum  paid  by  forest  A,  which  is  taxed  solely  on 
the  value  of  soil. 

Adding  compound  interest  to  these  annual  taxes  (Formula 
Ilia),  the  total  tax,  with  interest,  amounts  in  50  years  to  $86.53, 
equalling  51.3  per  cent  of  gross  stumpage  value,  or  53.4  per  cent 
of  net  cash  profit  on  stumpage.  But  basing  the  net  value  of 
the  stumpage  on  the  margin  over  costs  with  interest  or  $104.86, 
we  find  taxes  and  interest  absorbing  82.5  per  cent  of  this  margin. 

These  taxes  are  computed  as  follows: 
Let  e     =  annual  tax  on  original  assessed  value. 

e'    =  annual  tax  on  revaluation  at  20  years. 

e"  =  annual  tax  on  revaluation  at  30  years. 

e'"  =  annual  tax  on  revaluation  at  40  years. 

Then  £,£',£",£'"  =  —>  —  »  —  »  —  • 

o.op    o.op    o.op    o.op 

Sum  of  taxes  (Formula  Ilia), 

[l(E-i.op*>-E+Ef)i.opw-E"+E"fli.opw-E"+E'"]i.opw-E"r. 
$5.00  X  0.02  =  $0.10,  annual  taxes  for  20  years. 

—  =  $2.oo(E). 
0.05 

$2.00  X  2.6533  ~  $2.00  =  $3.30,  taxes  at  2oth  year. 
$22.81  X  0.02  =  $0.45,  annual  taxes  for  next  10  years. 

—  =  $9.12  (E'}  (discrepancy  due  to  decimal  values,  omitted 

in  text). 

$(3-30  +  9-12)  1.6289  -  $9-12  =  $11-12,  taxes  at  3oth  year. 
$66.14  X  0.02  =  $1.32,  annual  taxes  for  next  10  years. 


$(11.12  +  26.45)  1-6289  —  $26.45  =  $34-76,  taxes  at  40th  year. 


158  FOREST  VALUATION 

$113.91  X  0.02  =  $2.37,  annual  taxes  for  last  10  years. 

o^  =  $47.56  (£'").      . 

$(34.76  +  47.56)  1.6289  -  $47-56  =  $86. 53,  taxes  at  5oth  year. 
165.  Effect  of  the  General  Property  Tax  on  Forest  Production. 

—  The  effect  upon  the  owner's  profits  of  the  system  of  taxing 
sale  value  annually  depends  upon  the  length  of  time  the  present 
owner  has  held  the  property,  the  purchase  price,  the  amount 
of  back  taxes  already  paid  and  the  period  which  must  elapse 
previous  to  cutting.  The  relation  of  taxes  to  the  value  of  the 
property,  regardless  of  ownership,  is  independent  of  the  purchase 
price  or  of  back  taxes,  and  deals  only  with  the  future.  A  rapid 
rise  in  prices  for  timber  products  so  enhances  the  value  of  stand- 
ing timber  as  well  as  of  forest  soil  that  taxes  previously  paid, 
on  very  low  values,  do  not  absorb  an  unfair  percentage  of  pres- 
ent value.  Whatever  over-taxation  would  have  occurred  with 
stationary  values  has  been  offset  by  reason  of  this  increase  in 
capital  value  of  the  property.  A  continuous  increase  in  value 
of  forest  property  at  the  same  rate  as  in  the  past  would  continue 
to  absorb  a  large  portion  of  the  over-taxation  due  to  reassess- 
ments based  on  sale  value.  But  it  does  not  absorb  the  compound 
interest  item  which  accumulates  on  past  taxes  in  absence  of 
income  from  sales. 

Should  the  owner  have  paid  practically  no  taxes  up  to  the 
present  year,  he  can  pay  annually  on  full  value  for  a  definite 
period  before  the  amount  of  his  tax  with  interest  becomes 
equivalent  to  the  taxes  paid  on  forest  A.  Should  he  cut  his 
timber  sooner,  he  pays  less  than  this  tax.  For  every  year  which 
the  timber  stands  beyond  this  period,  the  tax  becomes  propor- 
tionally greater  than  its  just  equivalent. 

Assuming  that  the  tax  of  $41.97,  the  total  paid  in  50  years  on 
forest  A,  is  just,  how  long  can  an  owner  permit  his  timber  to 
stand  before  incurring  over-taxation.  The  sum  of  annual  taxes 
with  interest  must  equal  $41.97. 

E(i.opx  -  i)  =  41-97- 
Omitting  all  consideration  of  back  taxes,  the  results  are  as  follows : 


FOREST  TAXATION 


159 


TABLE   IV 

PERIODS  WITHIN  WHICH  PROPERTY  TAX  ON  TIMBER  BECOMES  EQUIVALENT 
TO  TAX  ON  SOIL  VALUE 


Age  of 
timber  at 
present. 

Present  value. 

Annual  tax 
2  per  cent  of 
present  value. 

Tax  capitalized 
(£). 

41.97  -i-  E,  or 
l.Opx  —  I. 

Period  indi- 
cated. 

Years 

Dollars 

Dollars 

Dollars 

Years 

50 

173-49 

3-47 

69.40 

0.6048 

9  to  10 

40 

113.91 

2.28 

45-56 

0.9212 

13  to  14 

3° 

66.50 

i-33 

26.60 

1-576 

19  tO  20 

20 

22.  8l 

0.46 

9-12 

4.600 

35  to  36 

The  indicated  period  is  found  by  looking  up  the  factor  i.opx 
in  the  table  of  values  for  5  per  cent  (Table  VI) .  The  value  cor- 
responding to  the  factor  is  found  opposite  the  year  indicating 
length  of  period. 

In  the  owner's  mind  these  periods  will  be  lengthened  if  he 
bases  his  standard  of  value  on  the  capital  value  of  the  forest 
rather  than  on  the  soil,  and  would  be  shortened  in  proportion  to 
the  back  taxes  which  he  has  paid.  Increasing  prices  for  forest 
products  would  lengthen  the  period,  and  future  increases  in  the 
assessed  value  of  the  property  would  shorten  it.  But  at  some 
future  date,  not  very  far  distant  for  mature  timber  when  taxed 
at  full  value,  the  timber  must  be  cut  or  the  process  of  confisca- 
tion begins.  After  the  year  in  which  the  accumulating  cost  of 
annual  taxes  equals  the  equitable  proportion  of  value  available 
for  taxation,  the  tax  steadily  confiscates  an  increasing  per  cent 
of  the  capital  value. 

With  the  tax  of  2  per  cent  on  soil  value,  the  per  cent  of  "net" 
income  appropriated  was  shown  to  be  40  per  cent.  This  in  effect 
appropriates  40  per  cent  of  Sv,  so  that  for  forest  land  worth 
$10.00  the  owner's  equity  amounts  to  but  $6.00,  and  the  state 
has  taken  $4.00  in  value  for  taxing  purposes. 

But  with  assessed  value  increased  at  lo-year  periods  the  per 
cent  of  the  net  future  income  taken  for  taxes  is  82.5  per  cent. 
Since  this  net  income  is  the  basis  of  capital  value  of  soil,  the 
state  thus  appropriates  $8.25  in  land  value,  leaving  the  owner 
a  residual  value  of  $1.75  exclusive  of  the  sum  required  to  reim- 
burse his  costs  and  taxes  with  interest  at  5  per  cent.  But  if  he 


160  FOREST  VALUATION 

has  paid  $5.00  for  this  land  he  cannot  afford  to  give  the  state 
in  taxes  two-thirds  of  this  cost  price  as  well  as  his  entire  net 
profit  over  5  per  cent.  Such  a  method  of  taxation  therefore 
tends  to  prevent  the  private  owner  from  undertaking  the  business 
of  forest  production. 

Upon  mature  timber  the  effect  is  to  stimulate  cutting  in  order 
to  save  taxes,  whether  or  not  over- taxation  has  already  occurred. 
Few  owners  stop  to  compute  how  much  taxes  timber  should  bear. 
They  know  that  the  way  to  escape  paying  any  more  taxes  is  to 
cut  the  timber.  If  this  is  the  purpose  of  the  tax  it  accomplishes 
its  object  thoroughly,  and  is  a  great  stimulus  to  over-produc- 
tion of  timber.  The  only  incentive  to  hold  mature  stumpage 
under  this  system  is  the  hope  that  increased  prices  will  offset 
the  taxes.  The  injurious  effects  of  a  bad  tax  system  are  not 
reflected  fully  by  depression  of  values  (§  153),  since  the  resulting 
losses  are  pocketed  by  the  owners  as  past  costs,  and  values  for 
stumpage  continue  to  reflect  only  future  elements  of  cost  and 
profit.  But  upon  the  business  of  lumbering,  in  a  region  of 
large  surplus  supplies  of  stumpage,  the  effect  is  disastrous,  forc- 
ing the  weaker  operators  into  bankruptcy  and  stimulating  rapid 
and  wasteful  cutting  on  the  part  of  even  the  strongest  holders. 

166.  Tax  Reform  for  Forest  Property.  —  From  the  analysis 
of  the  financial  relation  of  taxes  to  values,  the  most  serious  flaws 
in  the  system  of  taxing  forests  on  their  sale  value  appear  to  be: 

1.  Actual  over- taxation  through  taxing  annually  the  value  of 
the  entire  property  including  timber,  during  periods  when  no 
income  is  produced,  resulting  ultimately  in  confiscation  of  an 
inequitably  large  proportion  of  ultimate  or  total  income. 

2.  Uncertainty  as  to  the  extent  of  this  over- taxation  through 
the  arbitrary  power  vested  in  local  assessors  to  raise  valuations 
at  any  time. 

Tax  reform  must  remove  these  two  obstacles  by  substituting 
some  system  of  scientific  taxation  which  will  secure  equality 
between  forest  taxes  and  those  imposed  on  other  property  when 
gauged  by  the  per  cent  of  income  taken,  and  thus  remove  the 
element  of  uncertainty  which  is  even  worse  than  the  over-taxation 
itself. 


FOREST  TAXATION  161 

But  in  effecting  this  reform  the  annual  local  revenues  from 
taxation  must  be  maintained.  Reduced  revenue  at  present, 
even  if  made  up  in  later  years,  causes  heavier  taxation  of  other 
forms  of  property  (§  153).  This  is  the  explanation  of  the  failure 
of  many  attempts  to  encourage  forestry  by  granting  tax  rebates 
and  exemptions,  a  form  of  privilege  quickly  resented  and  ren- 
dered ineffectual  by  assessors  through  the  simple  device  of 
increasing  the  assessed  valuation  of  other  property  belonging 
to  the  beneficiary.  From  the  facts  discussed  in  Article  161  it 
appears  that  tax  reform  must  of  necessity  look  to  the  future 
rather  than  attempt  to  correct  past  errors.  On  this  basis,  the 
problem  divides  itself  into: 

The  taxation  of  forest  land  not  containing  merchantable 

trees. 
The  taxation  of  land  bearing  merchantable  timber. 

The  efforts  to  secure  an  equitable  tax  on  forest  land  devoid 
of  merchantable  timber  are  best  directed,  at  present,  along  the 
lines  discussed  in  Article  163.  A  combined  land  and  products 
tax  best  meets  the  needs  of  the  situation  and  is  most  easily 
understood.  It  must  not  be  forgotten  that  the  products  tax  is 
justified  only  when  land  is  not  taxed  at  its  full  value,  and  to  the 
extent  of  the  margin  of  accumulated  value  remaining  untaxed. 

Efforts  to  secure  this  result  have  recently  been  made  by  several 
states  in  the  northeast.  Connecticut  permits  no  increase  in 
assessed  value  of  land  for  fifty  years  and  limits  the  tax  rate  to 
10  mills.  An  additional  income  tax  of  10  per  cent  is  then  assessed 
on  the  stumpage  value  of  wood  products  when  harvested. 
Massachusetts  permits  the  revaluation  of  land  exclusive  of  timber 
at  any  time  so  that  it  is  probable  that  the  assessed  value  will 
be  raised  to  correspond  closely  with  expectation  value  of  the 
bare  soil.  Taxes  are  paid  annually  at  local  rates.  An  income 
tax  is  then  levied  on  forest  products  at  6  per  cent  of  the  stump- 
age  value.  This  tax  is  equitable  only  in  case  the  assessed  value 
of  land  will  average  lower  than  expectation  value,  to  an  extent 
sufficient  to  make  up  the  difference  represented  by  the  tax  on 
stumpage. 

Pennsylvania  arbitrarily  fixes  the  value  of  land  at  $1.00  per 


162  FOREST  VALUATIONS 

acre.  The  state  then  pays  local  taxes  at  2  per  cent  of  this  valu- 
ation, thus  assuming  the  burden  of  annual  taxation  for  the  joint 
benefit  of  the  owner  and  community.  These  taxes  are  never 
refunded  by  the  owner.  The  owner  pays  a  10  per  cent  stumpage 
tax  when  timber  is  cut. 

In  all  these  laws  only  land  voluntarily  offered  by  the  owner 
and  approved  by  the  state  forester,  or  in  Massachusetts  by 
the  local  assessors,  for  classification,  comes  within  the  operation 
of  the  law.  This  will  result  in  a  very  gradual  application  of 
the  system. 

No  valid  objection  can  be  urged  to  the  adoption  of  similar 
measures  in  any  region,  for  they  do  not  reduce  the  present  taxes 
and  will  result  in  greatly  increased  revenue  in  the  future  by 
bringing  into  productive  use  forest  lands  which  may  otherwise 
remain  waste. 

The  future  taxation  of  lands  bearing  merchantable  timber 
is  not  so  easily  provided  for.  The  immediate  substitution  of 
an  income  tax  which  takes  the  same  proportion  of  income  as 
the  existing  capital  tax  does  of  value,  is  entirely  impractical, 
owing  to  the  condition  of  the  capital  (§156).  Not  only  would 
the  annual  taxes  from  a  given  forest  vary  from  the  former 
amounts  paid  annually,  being  either  greater  or  less  according 
to  rapidity  of  logging,  but  this  variation  would  be  general;  and 
regions  where  logging  is  being  actively  conducted  would  be  in 
receipt  of  largely  increased  temporary  revenue,  while  districts 
as  yet  untouched  would  be  entirely  without  income  from  timber 
values.  Under  the  general  property  tax  the  local  revenue  is 
secured  only  as  long  as  the  timber  remains  standing,  after  which 
the  land  alone  may  be  taxed.  The  loss  of  current  revenue  after 
cutting  is  inevitable  under  any  system. 

A  plan  proposed  *  for  securing  equality  of  revenue  between 
counties,  for  conditions  prevalent  in  regions  of  heavy  virgin 
stands  and  large  operations,  contemplates  the  postponement 
of  the  annual  taxes  on  timber  until  the  timber  is  cut,  when  they 
will  be  paid  in  one  sum  but  without  compound  interest.  To 

*  Report  of  Forestry  Committee,  5th  Conservation  Congress,  November, 
1913,  page  128. 


FOREST  TAXATION  163 

equalize  local  revenues  the  state  shall  act  as  banker,  collecting 
the  tax,  advancing  funds  to  counties  as  yet  undeveloped,  and 
recouping  itself  from  counties  where  active  logging  is  in  process. 

In  eastern  states  a  different  plan  has  been  adopted.  Logging 
is  largely  in  second  growth  and  scattered,  so  that  the  problem  of 
equalizing  the  revenues  from  income  is  not  urgent.  The  plan 
is  to  continue  the  existing  valuation  of  property  containing 
timber  of  taxable  value,  but  to  permit  no  further  increase  in 
assessed  valuation  of  this  timber.  When  the  timber  is  cut, 
the  property  is  revalued  and  thereafter  taxed  only  on  the  value 
of  the  land.  In  Connecticut  this  protection  from  increased 
valuation  is  offset  by  a  slight  tax  on  yield,  increasing  i  per  cent 
for  each  decade,  for  50  years,  so  that  the  advantage  to  the  owner 
of  standing  timber  is  not  very  great. 

Massachusetts  has  adopted  a  plan  which  is  worthy  of  special 
mention.  The  land  containing  merchantable  timber  may  be 
revalued  at  time  of  classification  and  pays  a  land  tax  similar 
to  non-forested  land.  This  tax  is  subtracted  from  the  total 
tax  paid  on  the  entire  property  previous  to  classification.  The 
balance  is  the  additional  amount  of  tax  which  the  property 
must  continue  to  pay  if  local  revenues  are  to  be  maintained. 
This  is  termed  the  commutation  tax.  The  amount  of  this  tax 
cannot  be  subsequently  increased,  by  reason  of  increased  value. 
The  principle  is  that  the  timber  is  exempt  from  annual  taxation, 
yet  the  property  pays  this  commutation  tax  to  tide  over  the 
gap  between  the  present  year  and  the  receipt  of  the  income  tax. 
On  cutting,  the  timber  pays  a  10  per  cent  income  tax,  which 
extinguishes  the  commutation  tax.  A  particularly  valuable  pro- 
vision is  that  as  soon  as  timber  having  a  total  value  equal  to 
that  of  the  stumpage  originally  assessed,  has  paid  a  products 
tax,  the  timber  remaining  or  the  increase  resulting  from  growth 
is  freed  from  annual  taxation.  The  community  has  in  the  mean- 
time suffered  no  loss  of  local  revenue  and  is  in  receipt  of  an 
income  tax  in  lieu  of  increased  taxes  on  advancing  values. 

An  additional  advantage  of  this  plan  is  that  it  permits  of  the 
consolidation,  for  taxing  purposes,  of  areas  of  any  size  and  con- 
dition of  timber,  with  land  bare  of  merchantable  timber.  The 


164  FOREST  VALUATION 

amount  of  the  commutation  tax  is  made  a  lien  on  the  entire 
consolidated  tract  and  extinguished  by  cutting  on  any  portion 
of  it. 

Some  such  plan  of  taxation  is  recommended  as  possessing 
greater  merits  than  an  immediate  substitution  of  income  tax 
for  capital  tax  in  timbered  regions. 

No  law  providing  for  proper  taxation  of  forest  lands  should 
give  arbitrary  powers  to  a  state  official  to  prescribe  or  regulate 
the  scientific  methods  to  be  followed  by  the  owner  in  growing 
trees.  The  one  condition  to  be  insisted  on  must  be  that  the 
land,  especially  that  without  merchantable  timber,  shall  be 
brought  under  forest  cover  composed  of  useful  species,  and 
maintained  as  forest  land.  Cancellation  of  classification  should 
follow  failure  of  owners  to  comply  with  these  basic  conditions. 

To  prevent  owners  from  taking  advantage  of  such  laws  in 
order  to  escape  taxation  on  property  which  they  may  ultimately 
intend  for  some  other  purpose,  two  precautions  are  used:  the 
limitation  imposed  by  classification  of  lands  suitable  for  forest 
purposes,  and  provision  for  payment  of  a  penalty  upon  cancel- 
lation of  this  classification.  Connecticut  and  Vermont  prescribe 
that  lands  above  a  certain  value  per  acre,  not  including  timber 
values,  cannot  be  classified.  Massachusetts,  in  permitting  any 
lands  to  be  classified  regardless  of  value,  protects  the  public 
by  permitting  revaluations,  which  is  perhaps  the  better 
plan. 

On  cancellation  of  classification  the  penalty  imposed  should 
not  exceed  the  difference  saved  on  taxes  by  the  classification. 
Connecticut  determines  whether  the  property  at  time  of  cancel- 
lation has  increased  in  value  and  assesses  this  increase  at  one- 
half  the  average  rate  of  10  mills,  or  5  mills  per  year,  multiplied 
by  the  period  of  classification.  The  owner  thus  pays  his  back 
taxes  (without  interest),  on  the  theory  that  the  increase  has 
been  uniform  throughout  the  period.  Massachusetts  releases 
the  owner  by  the  payment  of  the  products  tax  on  all  timber 
standing  at  the  time  of  cancellation. 

The  apparent  difficulties  of  securing  the  adoption  of  rational 
tax  systems  for  forest  property,  not  the  least  of  which  are  the 


FOREST  TAXATION  165 

constitutional  provisions  of  many  states  requiring  all  property 
to  be  taxed  "equally"  under  the  general  property  tax,  should 
not  discourage  efforts  at  genuine  reform.  The  future  practice 
of  forestry  by  private  owners  must  be  accompanied  by  the 
adoption  of  a  reasonable  and  adequate  system  of  taxation  for 
forest  property. 


CHAPTER    XI 
STUMPAGE    VALUES 

167.  Definition   of   Stumpage  Value.  —  Stumpage  value  is 
the  sale  value  of  merchantable  standing  timber  —  its  value  on 
the  stump  previous  to  felling  and  removal.     The  term  "  mer- 
chantable "  is  not  so  easily  denned.     Timber  is  merchantable 
when  it  is  of  sufficient  size  to  furnish  wood  products  suitable 
for   definite   commercial   purposes.      There    can    be   no   fixed 
standard  of    sizes  to   coincide  with   the  general  definition  of 
"  merchantable  "  timber.     Trees  merchantable  for  cordwood  or 
paper  pulp  are  not  large  enough  to  yield  saw  timber.     It  follows 
that  stumpage  value  is  the  sale  value  of  timber  intended  for 
certain  specific  uses.     The  industry  which  can  pay  the  most 
for  the  timber  determines  its  stumpage  value.     In  the  form  of 
stumpage,  timber  is  a  portion  of  the  real  estate  (§§  134  to  136). 
When  purchased  with  land  it  may  be  held  indefinitely,  but  when 
bought  or  sold  separately  it  must  usually  be  removed  within  a 
stipulated  period.     The  value  of  stumpage  is  ordinarily  sepa- 
rated from  that  of  the  land,  even  when  both  are  purchased, 
though  in  the  past  the  land  was  often  considered  of  no  value 
except  for  the  timber. 

168.  Sale  Value  of  Stumpage.  —  Small  bodies  of  timber,  such 
as  woodlots,  are  frequently  sold  for  a  lump  sum.     The  value  of 
the  timber  is  thus  agreed  upon  without  determining  its  price 
per  unit,  which  is  known  only  to  the  purchaser  after  he  has  cut 
the  timber.     Areas  of  considerable  size   may  be  sold  on  the 
basis  of  a  price  per  acre. 

This  crude  method  is  giving  place,  for  large  tracts  or  timber 
aggregating  considerable  value,  to  the  determination  of  quantity 
and  agreement  upon  a  price  per  unit,  thus  arriving  at  total 
value.  But  neither  quantity  nor  price  are  easily  ascertained 

166 


STUMPAGE  VALUES  167 

for  standing  timber.  Products  already  harvested  and  measured, 
like  wheat  or  coal,  resemble  logs  or  lumber,  but  the  standing 
trees  are  like  the  grain  before  the  harvest,  or  the  coal  yet  in 
the  mine;  yet  not  quite  the  same,  for  the  trees  can  all  be  seen, 
and  their  contents,  quality  and  value  ascertained  with  some 
definiteness.  This  requires  agreement  upon  a  unit  of  measure- 
ment for  the  product,  as,  for  instance,  board  feet  by  a  given 
log  rule,  cords  or  posts.  The  methods  of  determining  the 
quantity  of  stumpage  are  discussed  in  Chapter  XIV. 

169.  Stumpage    Prices.  —  Prices    for    stumpage   are    deter- 
mined by  actual  sales,  whenever  a  price  per  unit  of  product  is 
quoted.     But  the  price  obtained  for  one  body  of  stumpage  is 
seldom  a  safe  basis  for  appraising  the  value  of  another  stand. 
For  no  other  product  is  there  such  need  of  checking  sale  values 
by  a   careful  appraisals  as  for  timber  stumpage.    Practically 
every  body  of  timber  should  have  a  separate  price,  determined 
by  the  factors  which  are  peculiar  to  the  stand  in  question. 
Standard  or  uniform  prices  are  often  established  in  a  region, 
for  small   bodies  of  stumpage  bought  by  a  single  company, 
but  this  uniformity  is  usually  explained  by  the  fact  that  the 
purchaser  is  in  position  to  dictate  the  price,  and  could,  if  he 
wished,  pay  more  for  the  better  lots. 

170.  Factors  Determining  Stumpage  Prices.  —  The  value  of 
stumpage  is  derived  directly  from  that  of  the  finished  products 
into  which  it  is  finally  manufactured  (§9).    The  stages  in  this 
process,  in  reverse  order,  are: 

Income  from          )  _ 
retail  lumber  ) 

Cost  of  retail  business 
Retailers  profits 
Freight  charges 

Cost  of  lumber      )  =  ^^  ^  manufacture  Qr  ^      = 
f  .o.b.  mills     ) 

Cost  of  manufacture 
Milling  profits 

Per  unit  of  product 

Overrun 
Cost  for  logs  at  mill  =  Income  from  logging  = 


l68  FOREST  VALUATION 

Cost  of  transportation 
Cost  of  felling  and  skidding 
Logging  profits 

„    .    ,   .  )   =  Income  from  timberlands,  or 

Cost  of  stumpage  { 

)       btumpage  value  = 

f  Cost  of  production,  or  carrying  charges 
{  Profits 

It  is  evident  that  the  gross  income  at  any  stage  in  this  eco- 
nomic series  just  equals  the  total  costs  plus  profits  incident  to 
the  entire  chain  of  processes  underlying  this  income  and  pre- 
ceding it  in  point  of  time,  and  that  the  profits,  or  losses,  are 
the  factors  which  balance  the  successive  equations.  Stumpage 
value  is  equivalent  to  cost  of  purchase,  and  tends  to  increase 
by  higher  prices  for  lumber,  and  to  decrease  by  higher  costs  or 
by  larger  profits  in  retailing,  manufacture  or  logging. 

There  may  be  a  great  difference  between  what  is  paid  for 
stumpage  and  what  should  be  paid.  This  difference  is  added 
to  the  profit  of  the  logger  or  lumberman  (§  168). 

But  actual  values  for  stumpage,  as  established  by  sales  of 
merchantable  timber,  do  not  fluctuate  with  the  annual  changes 
in  lumber  prices.  Increased  prices  for  lumber  are  not  imme- 
diately followed  by  similar  increases  in  stumpage  prices,  nor 
do  the  depressions  in  price,  which  are  so  characteristic  of  the 
lumber  trade,  make  themselves  felt  at  once  in  a  lowered  price 
for  stumpage.  Stumpage  prices  are  sluggish  rather  than  sen- 
sitive. 

Three  factors  serve  to  explain  this  apparent  failure  of  stump- 
age  to  behave  as  indicated  by  the  economic  relations  set  forth 
above.  The  first  is  the  human  element  in  price  making  (§§  5-7). 
At  best,  it  takes  an  expert  thoroughly  familiar  with  the  costs  and 
reasonable  profits  of  such  technical  and  diversified  industries  as 
logging  and  milling  to  determine  the  proper  relations  between 
prices  f.o.b.  at  mill  for  lumber  and  prices  for  stumpage.  The 
purchaser  possesses  this  knowledge  but  the  stumpage  owner 
may  not  have  it.  Since  it  is  to  the  purchaser's  interest  to  keep 
the  owner  in  ignorance,  prices  are  allowed  to  remain  as  long  as 
possible  at  the  level  set  by  previous  sales.  This  condition  is 
disturbed  only  when  competition  between  two  purchasers  brings 


STUMPAGE  VALUES  169 

prices  up  to  their  proper  level  to  the  benefit  of  the  stumpage 
owners.  The  same  condition  is  secured  when  timber  is 
sold  by  a  lumber  company  which  is  fully  acquainted  with  its 
value. 

The  second  factor  is  the  controlling  influence  of  transportation 
and  logging  costs.  Logging  alone  frequently  requires  a  large 
investment  in  railroads,  flumes  and  equipment.  It  is  often  im- 
possible for  the  owner  of  a  small  body  of  timber  to  market  it, 
except  by  means  of  the  facilities  owned  by  a  lumber  company. 
The  owner  feels  entitled  to  the  stumpage  value  which  results 
from  these  increased  transportation  facilities.  The  lumberman 
endeavors  to  secure  the  stumpage  at  the  value  which  it  had 
before  his  improvements  were  constructed.  When  he  is  the 
only  purchaser,  his  price,  rather  than  that  desired  by  the 
owners,  is  usually  determined  upon  as  the  value  of  the 
stumpage. 

The  third  factor  is  the  element  of  time.  Present  prices  of 
finished  lumber  can  under  no  circumstances  determine  present 
stumpage  prices  absolutely.  In  the  first  place  they  do  not 
apply  to  present  but  to  past  stumpage  values,  and  the  value  of 
present  stumpage  will  depend  upon  the  price  obtained  when 
its  product,  in  turn,  reaches  the  market  (§  n). 

But  the  period  required  to  bring  the  timber  from  the  stump 
to  the  retailer,  or  even  to  the  cars,  is  not  the  most  important 
element  of  time  involved,  and  neither  the  discount  factor  nor 
the  speculative  probability  of  a  change  in  value  for  this  short 
period  would  have  much  influence  on  stumpage  prices.  A 
more  important  fact  is  that  large  bodies  of  stumpage  cannot 
be  logged  at  one  time.  The  operation  must  extend  over  several 
years.  Therefore  the  prices  finally  received  for  this  lumber  will 
not  be  this  year's  or  next  year's  prices,  but  an  average  of  many 
years.  Averages  tend  to  eliminate  annual  fluctuations.  Stump- 
age  values  do  not  fall  when  lumber  prices  decline  because  the 
owners  of  stumpage  expect  that  before  they  have  finished  cutting, 
these  lumber  prices  will  have  risen  again. 

171.  Appraisals  of  Stumpage  Value.  —  An  appraisal  of 
stumpage  value  requires: 


170  FOREST  VALUATION 

(a)  Acceptance  of  a  definite  class  of  products  or  stage  of 
manufacture  as  furnishing  a  basis  of  prices  from  which  to  under- 
take the  appraisal.  The  further  removed  this  basis  is  from 
stumpage  value,  the  greater  will  be  the  difficulty  of  correctly 
appraising  the  intervening  elements  of  cost  and  profit.  But 
the  more  stable  and  widely  accepted  are  the  prices  which  fur- 
nish this  basis,  the  more  reliable  will  be  the  result. 

(&)  Appraisal  of  expenses  of  the  intervening  operations  as 
logging,  or  logging  and  milling,  including  depreciation  of  capital 
assets  employed  in  these  enterprises. 

(c)  Determination  of  legitimate  profits  for  logging  and  mill- 
ing, and  of  the  proper  basis  and  method  of  computing  what 
such  profits  should  be. 

(d)  Residual  or  stumpage  value  after  subtracting  elements 
b    and   c   from    a,    and    correcting    for    the    error    caused    by 
overrun,   in  order  to  express  value  of  stumpage  in  terms  of 
log  scale. 

172.  The  Price  Basis  in  Appraisals.  —  The  acceptance  of  the 
retailer's  price  as  the  starting  point  for  appraising  stumpage 
values  would  interpose  retail  costs  and  profits  as  an  element 
in  the  appraisal.  This  would  result  in  appraising  the  value 
of  lumber  f.o.b.  cars  at  mill,  instead  of  accepting  the  current 
prices  already  determined  for  this  lumber  by  sales;  such  a  course 
is  obviously  undesirable. 

Were  the  prices  of  logs  standardized,  and  determined  in  open 
competitive  market  as  are  wholesale  lumber  prices,  there  would 
be  a  similar  argument  for  accepting  log  prices  instead  of  sub- 
stituting an  appraisal  of  the  value  of  logs.  This  method  has 
been  used  on  Puget  Sound  where  such  a  log  market  exists. 
Whenever  logging  is  conducted  as  a  separate  business,  and  not 
merely  by  contract  for  the  manufacturer,  the  price  of  logs  does 
determine  what  may  be  paid  for  stumpage,  and  must  be  taken 
as  the  basis  of  appraisals. 

It  is  claimed  that  in  markets  established  for  logs,  prices  for 
the  logs  are  not  as  high  as  an  equitable  appraisal  would  indicate 
owing  to  the  ability  of  the  mill  owners  to  keep  these  prices 
under  control.  Where  the  log  market  is  the  only  outlet  for  the 


STUMPAGE  VALUES  171 

logs,  this  fact  would  not  justify  an  appraisal  of  stumpage  based 
on  higher  log  prices,  unobtainable  in  practice,  although  it  might 
justify  holding  rather  than  selling  the  timber. 

But  in  the  majority  of  cases,  the  business  of  logging  is  either 
conducted  by  the  same  firms  which  manufacture  the  timber, 
or  the  manufacturer  purchases  the  stumpage,  contracts  the  log- 
ging and  thus  bases  the  price  which  he  can  pay  for  the  stumpage 
on  the  price  of  lumber  at  the  mill.  Stumpage  appraisals  must 
thus  conform  strictly  to  the  prevalent  economic  conditions,  and 
must  be  based  on  the  value  of  the  product  put  forth  by  the 
operator  who  purchases  the  timber,  provided  he  conforms  to 
general  customs  in  the  locality. 

Mill  prices  for  lumber  fluctuate  not  only  with  the  season 
and  condition  of  the  market,  but  are  affected  by  freight  charges. 
In  certain  localities,  prices  at  large  central  markets  for  lumber 
may  be  taken  as  standard,  and  the  proper  discounts  made  for 
local  freight  rates. 

The  main  source  of  variation  in  mill  prices  lies  in  the  variety 
of  products,  and  of  grades  of  the  same  product,  into  which  the 
timber  is  manufactured.  This  difference  exists  originally  in 
the  quality  of  the  trees  or  logs,  and  is  increased  by  the  methods 
of  handling  the  raw  material  or  logs  by  the  millman.  One  mill 
may,  from  the  same  material,*  produce  a  much  greater  per  cent 
of  the  more  valuable  grades  than  another,  whose  principal  out- 
put may  be  dimension  lumber. 

These  differences  in  the  quality  of  the  grades  produced  vitally 
affect  stumpage  value  and  give  to  old  timber  a  value  at  present 
prices  which  second  growth  timber  may  never  obtain  hi  the 
future  because  of  inferior  quality. 

Two  plans  may  be  used  in  obtaining  a  price  basis  for  the 
appraisal  of  a  given  body  of  stumpage.  The  first,  advocated 
by  the  U.  S.  Forest  Service  in  Washington  and  Oregon,  is  based 
on  grade  prices  at  a  central  market,  discounted  for  freight 
rates  to  the  required  locality. 

The  first  step  is  to  estimate  in  the  field  the  per  cent  of  each 
of  certain  standard  grades  which  will  probably  be  yielded  by 
the  body  of  timber  to  be  appraised.  The  average  price  of  each 


172  FOREST  VALUATION 

grade  is  obtained  and  a  per  cent  of  this  price  taken  equal  to  the 
per  cent  of  the  total  stand  represented  by  the  given  grade. 
These  fractional  prices,  when  totalled,  give  an  average  price 
weighted  both  by  quantity  and  value  for  the  grades  ex- 
pected.* 

The  second  plan  depends  upon  "mill  run"  prices.  In  the 
absence  of  stable  central  markets,  average  prices  for  the  total 
output  of  mills,  termed  mill  run  prices,  are  advocated.  This 
method  is  defective  for  several  reasons.  The  higher  the  average 
prices  for  lumber,  the  more  profitable  it  becomes  to  manufacture 
low  grades.  In  periods  of  depression  these  grades  may  be  left 
to  waste  hi  the  woods.  An  increased  output  of  cheap  grades, 
which  always  follows  higher  prices,  may  actually  lower  rather 
than  raise  the  average  mill  run  prices  for  lumber.  Again,  when 
prices  are  based  on  average  mill  run,  the  per  cent  of  grades 
sawed  may  not  coincide  with  those  which  can  be  produced  from 
the  timber  to  be  appraised,  either  because  the  mill  may  have 
been  cutting  in  timber  better  or  poorer  than  the  average,  or, 
because  the  timber  to  be  appraised  may  be  better  or  poorer 
than  the  average.  Mill  run  prices  for  timber  known  to  be  of 

*  The  following  figures,  used  in  determining  the  average  price  of  lumber  in  con- 
nection with  a  recent  timber  sale  in  Washington,  were  furnished  by  Asst.  District 
Forester,  F.  E.  Ames,  U.  S.  Forest  Service,  and  serve  to  illustrate  this  method. 

DOUGLAS  FIR  GRADES,  PRICES  AND  AVERAGE  VALUE 

No.  i  V.  G.  Flooring 3%  @  $26.00  $0.78 

No.  2  V.  G.  Flooring 5%  @  23.00  1.15 

No.  2  and  Bet.  F.  G.  Flooring 3%  @  15.00  .45 

No.  2  Clear  and  Bet.  Finish 5%  @  26.00  1.30 

No.  2  Clear  and  Bet.  Siding  and  Rustic. .   4%  @  17.00  .68 

No.  3  Clear  Flooring.     Siding  and  Rustic  8%  @  13.50  1.08 

No.  i  Shop 4%  @  16.00  .64 

Car  Sills 6%  @  16.50  .99 

Timbers 15%  @  10.30  1.55 

Dimension 28%  @  9.10  2.55 

Boards  and  Shiplap 12%  @  8.75  1.05 

Dunnage 7%  @  6.00  .42 

$12.64 

The  grade  prices  represent  the  average  of  the  quarterly  averages  from  July  i, 
1911  to  July  i,  1914.  Underweights  not  included. 


STUMPAGE  VALUES  173 

similar  quality  to  that  appraised  removes  this  objection.  Aver- 
age mill  run  prices  for  several  mills  in  a  region  are  serviceable 
only  when  the  timber  is  remarkably  uniform  in  quality  and 
grade. 

173.  Depreciation.  —  Depreciation  plays  so  much  more  im- 
portant a  part  in  stumpage  appraisals  than  in  forest  pro- 
duction that  it  should  be  given  special  consideration  in  this 
chapter. 

Depreciation  is  a  sum  written  off  or  subtracted  from  the  cost 
of  capital  assets,  to  correspond  roughly  or  approximately  with 
a  shrinkage  or  disappearance  of  value  through  diminishing  use- 
fulness. An  investment  in  a  fixed  or  durable  asset  is  not  an 
"expense  "  at  the  time  of  purchase,  but  an  exchange  of  cash  for 
another  form  of  property.  The  real  expense  is  incidental  to 
the  use  or  service  which  this  property  yields,  by  reason  of  which 
it  diminishes  in  value.  Depreciation  on  property  for  which 
there  exists  a  continuous  need  corresponds  to  actual  deteri- 
oration and  final  discarding  of  the  article  as  worn  out.  But 
where  the  period  and  amount  of  use  is  limited  and  the  property 
will  outlast  its  usefulness,  the  residual  value  will  coincide  with 
the  value  of  the  material  of  which  it  is  composed,  for  removal 
or  use  in  some  other  line.  This  shrinkage  in  value  not  accom- 
panied by  physical  deterioration  may  be  termed  "amortiza- 
tion." 

When  depreciation  is  added  to  other  expenses,  the  sum  gives 
the  total  actual  outlay  or  cost  of  the  business,  in  which  total 
the  investment  in  capital  assets  subject  to  depreciation  is  ex- 
cluded, as  not  constituting  a  cost. 

A  depreciation  fund  is  a  fund  created  by  the  setting  aside 
annually,  from  net  income,  amounts  intended  to  eventually 
equal  the  total  depreciation  (§  73).  When  the  period  is  known 
with  reasonable  certainty,  the  amounts  annually  needed  to 
accomplish  this  purpose  can  be  computed  in  advance. 

Let  A  =  original  capital  investment. 

W  =  final  or  wrecking  value. 
D  =  total  depreciation  or  A  —  W. 
n  =  years  in  period. 


174  FOREST  VALUATION 

Four  methods  may  be  used  in  determining  depreciation. 

Method  A.  The  total  depreciation  may  be  refunded  by  de- 
positing each  year  in  a  savings  bank,  at  p  per  cent,  or  investing 
and  reinvesting,  annual  sums  in  such  a  way  as  to  earn  compound 
interest,  so  that  the  total  of  principal  and  interest  at  the  end 
of  the  period  equals  the  depreciation.  This  fund  is  not  returned 
to  the  owners  until  the  expiration  of  the  period.  Their  capital 
investment  remains  at  its  original  figure,  and  the  annual  divi- 
dends are  declared  on  this  basis. 

Let  X  =  annual  sum  for  depreciation. 

Then  —  (i.opn-  i)  =  D,     (See  III.) 

o.op 


This  method  is  seldom,  if  ever,  employed  in  connection  with 
annual  business,  although  it  is  practical  as  the  basis  of  a  sinking 
fund  for  the  payment  of  bonds. 

The  other  three  methods  neglect  the  factor  of  compound 
interest  on  the  annual  payments,  and  undertake  to  repay, 
through  a  series  of  years,  sums  whose  cash  total  will  just  equal 
the  total  depreciation. 

Method  B.  This  method  proposes  to  pay  the  total  depre- 
ciation in  equal  annual  instalments  covering  the  requisite 
period.  The  formula  is 

„      D  A  -W  /Tt. 

X  =  -     or  —  •  (PO 

n  n 

The  method  is  used  more  widely  than  any  other  and  is  easily 
understood  and  applied.  Actual  return  to  investors  of  this 
annual  appropriation  for  depreciation  would  have  the  result  of 
diminishing  the  capital  investment  annually. 

Method  C.  Instead  of  depreciating  the  capital  by  equal 
amounts  annually,  the  depreciation  may  be  made  to  equal  a 
fixed  per  cent  annually  of  the  residual  value  of  the  capital; 
its  value  less  previous  depreciation.  By  this  means,  depre- 


STUMPAGE  VALUES  175 

elation  expense  is  heaviest  in  the  earlier  years,  and  steadily 
diminishes. 

Let  z  =  per  cent  of  depreciation,  and 

o.oz  =  per  cent  expressed  decimally. 

Then       A(i  -  o.oz)n  =  W, 


O.OZ  =   I   -  t, 

A 


This  method  is  seldom  employed  as  it  is  inconvenient  to  write 
off  large  sums  for  depreciation  in  the  earlier  stages  of  the  business, 
especially  in  lumbering. 

Method  D.  This  method  proposes  to  increase  the  amount 
charged  to  depreciation  annually,  and  combine  it  with  an  annual 
interest  return  on  the  diminished  or  residual  capital,  in  such 
amounts  that  the  sum  of  interest  and  depreciation  will  require 
equal  annual  payments.  Depreciation,  by  reducing  the  invested 
capital,  correspondingly  lowers  the  interest  returns  required 
by  a  given  rate  of  interest.  This  reduction  in  interest  may  be 
added  annually  to  depreciation.  It  only  remains  to  determine 
what  annual  sum  in  excess  of  interest  on  the  original  investment 
is  required  for  the  first  payment,  to  secure  this  balance  between 
the  two  elements  of  interest  and  depreciation,  so  that  the 
sum  of  the  increasing  payments  on  account  of  depreciation  will 
at  the  close  of  the  period  just  equal  the  total  amount  to  be 
written  off. 

In  this  case,  either  of  two  solutions  is  possible  to  determine  the 
annual  payment. 

Let  Z  =  annual  payment  for  interest  and  depreciation. 

Let  d  =  ^^-  -  -  ,  when  p  =  rate  of  interest  to  be  earned  on 
o.op 

capital  A. 


176  FOREST  VALUATION 

Then  z^d.or)-^  (P3) 

or  -     Z  =  A(o.op)+~^  (P4) 

a 

The  first  formula  utilizes  the  wrecking  value,  while  the 
second  introduces  total  depreciation,  and  is  somewhat  simpler. 
The  factor  d  is  easily  computed  from  Table  VI,  or,  for  values  of 
p  not  given,  by  logarithms,  in  which  the  logarithm  of  i.op  is 
multiplied  by  n  to  obtain  the  logarithm  of  i.opn.% 

*  "Modern  Accounting,"  by  Henry  Rand  Hatfield,  page  132. 

\  (A  •  i.op  —  X)  i.op  —  X]  i.op  ...  to  w  terms  =  W. 
A  (i.opn)  -X(i  +  i.op  +  i.op2  .  .  .  Lop"-1)  =  W. 

A  (i.opn)  -  X  T-°pn  ~  T  =  W  (by  Formula  Qj). 
i.op  —  i 

x_A(i.opn)-W 
i.opn—  i 

op 
A  (i.opn)  -  W 

d 

t  Proposed  by  W.  B.  Hunter,  formerly  special  examiner  in  U.  S.  Bureau  of 
Corporations. 

Let  X  =  A  (o.op)  +  e. ' 

Then,  in  second  year, 

(A  -  o.op  —  e)  o.op  =  interest  on  capital. 
e  (o.op}  =  increase  in  depreciation. 
e  +  e  (o.op)  =  e(i.op)  =  depreciation. 
In  third  year, 

(A  •  o.op  —  e  '  i.op)  o.op  =  interest. 

e  (i.op)  X  o.op  =  increase  in  depreciation. 

e  (i.op)  —  e  (i.op)  X  o.op  =  e  (i.op2),  depreciation. 

D  =  e  +  e  (i.op)  +  e  (i.op*)  .  .  . 


A  (o.op)  +. 

i  The  objections  urged  against  this  method  are:  first,  that  it  allows  interest  on 
invested  capital  as  a  cost  (Hatfield);  second,  that  a  plant  depreciates  more  rap- 
idly during  the  first  few  years  than  thereafter,  and  loss  during  that  time  would 


STUMPAGE  VALUES  177 

174.  Milling  Costs  and  Profits.  —  The  cost  of  milling  or 
manufacture  may  be  standardized  for  operations  of  a  given 
size.  The  current  expenses,  or  operating  costs,  do  not  vary 
greatly.  For  operations  involving  a  definite  quantity  of  stump- 
age,  the  duration  of  the  operation  is  largely  determined  by  the 
capacity  of  the  mill. 

The  factor  which  indicates  the  most  profitable  size  for  a  mill 
is  the  relation  between  the  depreciation  of  fixed  costs  or  capital 
expenditures  for  the  plant  and  machinery,  and  the  period  and 
quantity  of  output  over  which  this  cost  must  be  distributed. 
The  value  of  the  mill  when  there  is  no  more  timber  to  cut  is 
practically  nothing,  and  that  of  second-hand  machinery,  very 
small.  The  difference  between  these  final  values  and  initial 
cost,  which  represents  depreciation,  is  one  of  the  principal 
elements  of  expense  (§  173). 

The  size  of  this  item  of  depreciation  and  the  relation  which  it 
bears  to  the  total  output,  and  to  the  total  cost  of  producing 
each  unit  of  product,  evidently  depends  more  upon  the  total 
length  of  time  over  which  the  plant  can  continue  to  operate 
than  upon  its  daily  capacity.  With  mills  of  equal  efficiency, 
the  one  with  a  twenty-year  cut  may  be  considered  as  having 
about  half  the  depreciation  expense  per  unit  of  output  that  one 
with  but  ten  years'  cut  must  write  off. 

Provided  the  supply  of  logs  is  assured,  and  the  period  over 
which  to  distribute  the  cost  of  depreciation  can  be  approxi- 
mated, the  requisite  profits  in  manufacturing  may  be  gauged 
with  reasonable  uniformity.  Uncertainty  as  to  future  timber 
supply  makes  it  necessary  to  guard  against  a  shortage  or  com- 
plete exhaustion  of  raw  material  by  a  correspondingly  large 
appropriation  from  gross  income  for  depreciation.  Should 
this  shortage  not  materialize,  the  concern  would  later  find  its 

find  the  proprietors  without  adequate  provision  for  meeting  this  loss.  The  first 
objection  does  not  apply  when  the  purpose  of  the  computation  is  to  determine 
profits  in  advance,  since  these  are  not  treated  as  costs.  The  second  objection 
holds  good  if  it  is  considered  necessary  to  make  the  amounts  written  off  for  de- 
preciation agree  closely  with  actual  loss  in  value.  The  results  obtained  by 
this  method  agree  more  closely  with  those  of  Method  A  than  with  Method 
BorC. 


178  FOREST  VALUATION 

financial  position  and  average  profits  correspondingly,  and  justly, 
increased  by  these  earlier  sacrifices. 

The  costs  and  profits  of  manufacture  are  both  included  in 
contract  prices  for  sawing  or  manufacturing  products,  which 
is  the  basis  of  operations  of  many  portable  saw  mills. 

175.  Logging  Costs  and  Profits.  —  It  is  in  the  logging,  rather 
than  the  milling  end  of  lumbering,  that  the  greatest  variations 
in  costs  occur.  The  cost  of  felling  and  bucking  the  trees  into 
logs,  ties  or  poles  may  be  standardized.  But  the  cost  of  trans- 
portation of  the  product  from  the  site  to  the  mill  is  determined 
by  a  number  of  exceedingly  variable  factors,  and  is  the  prin- 
cipal part  of  logging. 

These  factors  are:  accessibility  and  quantity  of  stumpage, 
and  methods  of  transportation  adapted  to  climate,  to  the  topog- 
raphy and  to  the  size  of  the  timber.  The  direct  relation  of  total 
quantity  or  volume  upon  the  cost  per  unit  of  the  combined 
expense  of  constructing  the  transportation  routes  and  moving 
the  product  needs  to  be  emphasized  (§98),  and  explains  the 
great  differences  in  value  of  timber  of  equal  quality  but  differing 
merely  in  quantity  available. 

Accessibility  is  a  relative  condition  depending  upon  the  total 
cost  per  unit  of  product  to  bring  the  timber  to  the  mill,  and  the 
margin  of  profit  remaining  for  distribution  between  the  owner 
of  stumpage  and  the  logger.  When  the  logger  sees  so  small  a 
margin  that  he  demands  it  all,  the  timber  is  for  the  present 
inaccessible.  Accessibility  depends,  then,  upon  the  total  volume 
available  as  well  as  upon  the  location  of  the  site  and  the  diffi- 
culties and  costs  of  transportation  intervening  between  site  and 
mill. 

Methods  of  transportation  exercise  a  profound  influence 
upon  logging  costs.  The  factor  of  climate  exerts  its  chief  influ- 
ence upon  the  bottom,  making  ice  roads  possible  in  some  regions, 
while  in  others  rain  greatly  increases  the  difficulties  by  soften- 
ing the  soil.  The  driving  of  streams,  supplemented  by  the 
sleigh  haul,  may  be  superseded  by  rail  transportation  involving 
an  investment  of  an  entirely  different  character.  For  short 
distances,  in  regions  of  second  growth,  wagon  haul  is  the  chief 


STUMPAGE  VALUES  179 

dependence  of  the  operator.  The  overhead  cable  to  supple- 
ment the  railroad  may  prove  cheapest,  as  hi  cypress  swamps  or 
over  broken  gorges,  while  elsewhere,  skidding  by  ground  cables 
or  with  animals  is  most  efficient. 

In  appraisals,  average  logging  costs  for  the  specific  body  of 
timber,  based  on  the  methods  accepted  by  experience  in  that 
region  as  best  and  cheapest,  will  be  the  basis  of  costs.  Excessive 
costs  due  to  deliberate  use  of  methods  shown  to  be  antiquated 
or  expensive,  when  the  operator  is  in  position  to  use  better 
methods,  or  when  others  can  be  found  who  will  do  so,  cannot 
be  permitted  to  influence  or  increase  the  factor  of  logging  costs. 
An  additional  cost  is  incurred  in  logging  under  forestry  prin- 
ciples (§§  107  and  176). 

The  profits  in  logging  are  less  easily  gauged  than  in  milling. 
The  great  variation  in  conditions,  which  makes  each  logging  job 
or  "chance"  a  separate  venture,  prevents  the  standardization 
of  methods  and  increases  the  uncertainty  of  the  total  estimated 
cost,  and  consequently  of  the  risk  of  loss.  Added  to  this  is 
the  risk  from  natural  agencies,  as  floods,  fire,  drought,  lack  of 
cold  weather,  too  much  snow  or  any  other  variation  from  normal 
which  either  directly  damages  the  timber  or  the  means  of  trans- 
portation, or  unduly  increases  the  labor  and  cost  of  logging. 

Logging  work  is  less  closely  supervised  from  the  main  office 
than  is  milling.  Hence  woods  bosses  are  more  largely  thrown 
on  their  own  resources.  The  main  attributes  of  woods  foremen 
even  now  is  brute  force  and  practical  experience.  This  type 
of  boss  lacks  ability  to  apply  methods  of  scientific  efficiency. 
The  average  risk  in  logging  is  probably  double  that  incurred 
in  manufacture. 

Depreciation  as  an  item  of  expense  in  logging  chiefly  concerns 
the  means  of  transportation.  The  entire  initial  cost  for  tempo- 
rary railroads,  flumes  or  roads,  which  will  be  abandoned  on  com- 
pletion of  the  operation,  is  depreciated  or  charged  off  as  a  cost 
of  logging.  The  costs  for  railroads,  or  roads  which  will  after- 
wards be  used  for  permanent  traffic,  will  be  maintenance  and 
the  difference  in  value  of  the  road  at  the  beginning  and  end 
of  the  operation.  A  logging  company  which  subsequently  sells 


l8o  FOREST  VALUATION 

the  road  to  a  railroad  company  for  continuous  operation  may 
secure  a  price  equal  to  the  cost  of  the  road,  in  which  case  no 
depreciation  is  incurred.  Such  a  result  cannot  be  assumed,  and 
depreciation  must  always  be  charged  against  the  transportation 
system. 

The  cost  of  all  logging  equipment,  such  as  cables,  engines, 
horses,  and  other  supplies,  should  be  reckoned  not  in  the  form 
of  a  capital  expenditure  but  as  depreciation. 

176.  Stumpage  as  a  Capital  Investment  and  as  a  Cost  of  Raw 
Materials.  —  Methods  of  appraising  the  value  of  stumpage  on 
the  basis  of  the  present  net  residue,  after  subtracting  logging 
and  manufacturing  costs  and  profits,  are  based  on  the  supposi- 
tion that  this  timber  will  be  removed  within  a  short  time,  not 
exceeding  three  to  five  years.  Such  values  are  applicable  to 
short-term  contracts  or  to  small  bodies  of  timber,  and  to  pur- 
chases in  which  land  is  not  included.  But  the  purchase  for 
cash  of  large  bodies  of  stumpage  introduces  an  additional  ele- 
ment of  cost  which  must  be  considered  by  the  purchaser.  The 
time  which  must  elapse  previous  to  the  actual  completion  of 
cutting  necessitates  the  holding  of  this  stumpage,  with  accom- 
panying annual  expenses  (§  170).  This  would  apparently  lower 
the  price  the  purchaser  can  pay,  in  the  same  manner  that  the 
absence  of  a  market  at  present,  even  if  it  is  sure  to  develop 
later,  depresses  present  values.  When  transportation  facilities, 
mills  and  markets  are  ready,  the  price  will  be  correspondingly 
higher  than  in  regions  where  development  must  follow  purchase. 

It  is  not  possible,  however,  to  arrive  at  a  proper  appraised 
value  for  large  areas  of  standing  timber  by  the  method  of  com- 
puting the  value  for  immediate  cutting,  and  then  discounting 
this  value  for  the  average  period  which  the  timber  must 
stand. 

In  spite  of  the  impossibility  of  immediate  cutting,  the  timber 
will  usually  sell  for  the  value  shown  without  such  discount. 
This  is  explained  by  the  element  of  increasing  prices,  to  which 
may  be  added  growth  of  timber  and  improvement  in  quality. 
It  would  be  unfair  to  discount  a  future  stumpage  value  based 
on  present  sales,  when  everyone,  purchaser  and  owner  alike, 


STUMPAGE  VALUES  l8l 

expects  stumpage  to  increase  in  value  (§  188).  Were  it  definitely 
known  that  no  such  increase  would  occur,  the  expectation  value 
of  the  revenue  from  cutting  the  timber  would  be  less  than  the 
present  sale  value  for  immediate  cutting.  As  it  is,  the  expec- 
tation value  of  the  stumpage  is  based  on  this  probable  increase 
and  its  present  sale  value  is  not  depressed  by  the  postponement 
of  cutting.  Again,  the  great  advantages  accompanying  the 
ownership  of  large  bodies  of  timber  and  the  reduction  of  depre- 
ciation costs  (§  173)  and  transportation  charges  (§  174)  in  them- 
selves more  than  offset  such  possible  discount  in  value. 

The  value  of  stumpage  for  immediate  purchase  as  a  capital 
investment  may  therefore  be  appraised  on  the  basis  of  what 
it  is  worth  on  the  completion  of  the  necessary  transportation 
and  milling  facilities,  or,  if  these  are  assured,  it  may  safely  be 
based  on  present  value. 

For  stumpage  which  is  paid  for  in  small  instalments  just 
previous  to  or  following  the  cutting  of  the  timber,  the  value  is 
manifestly  that  existing  at  the  time  of  payment.  On  long-term 
contracts,  as  a  result  of  such  postponed  payments,  a  readjust- 
ment of  stumpage  values  is  required  at  reasonable  intervals, 
on  account  of  the  expected  increase  in  future  prices  of  lumber. 
This  method  of  payment,  by  which  the  operator  is  relieved  not 
only  of  the  investment  with  its  attendant  annual  expense,  but 
also  of  the  risk,  and  of  any  losses  which  may  result  from  fire 
or  any  other  agency,  puts  stumpage  in  the  same  class  as  that 
of  raw  materials,  rather  than  capital.  The  attendant  advan- 
tages to  the  purchaser,  corresponding  to  the  prospective  loss 
and  risk  of  holding'  timber,  are  recognized  as  having  a  value 
great  enough  to  form  a  material  inducement  in  sales  of  timber 
on  National  Forests.  It  is  usually  sufficient  to  offset  the  addi- 
tional cost  of  brush  burning  and  other  silvicultural  measures 
required  by  the  government. 

177.  The  Determination  of  Legitimate  Profits.  Overturn 
Methods.  —  Costs  must  be  gauged  in  relation  to  the  quantity  of 
product  resulting  from  a  given  expenditure,  and  a  cost  account 
seeks  to  determine  the  cost  and  the  resulting  profit  on  each 
unit  (§25).  All  factors  of  cost,  including  depreciation,  may  be 


182  FOREST  VALUATION 

expressed  on  the  basis  of  a  thousand  board  feet,  cord  or  other 
unit  of  product. 

The  surplus  after  subtracting  costs  from  the  average  price 
of  the  product  is  the  net  profit,  from  which  is  paid  the  returns 
on  the  invested  capital  and  the  enterpriser's  gain  for  services 
(§39).  If  the  cost  of  stumpage  is  fixed,  this,  added  to  other 
costs,  determines  the  logger's  profit.  In  appraisals  of  stumpage, 
on  the  other  hand,  the  net  surplus  after  paying  all  other  expenses 
must  "be  divided  between  stumpage  and  profit,  and  the  deter- 
mination of  legitimate  profit  must  precede  that  of  stumpage 
value. 

On  small  ventures,  where  the  enterpriser  depends  almost  en- 
tirely on  his  individual  efforts  and  the  amount  of  capital  invested 
is  insignificant,  most  of  the  annual  costs  are  met  from  income, 
depreciation  is  a  small  item,  and  profit  is  usually  gauged  by  the 
margin  of  income  over  costs  for  each  unit.  Logging  contractors 
are  satisfied  if  they  realize,  say,  $i  profit  per  thousand  board 
feet  log  scale  above  their  computed  expenses.  Profits  may 
always  be  expressed  in  this  manner,  whether  or  not  the  calcula- 
tion stops  at  this  point.  This  has  been  termed  the  overturn 
method  of  expressing  profits,  since  the  working  capital  used  for 
wages  and  other  current  expenses  is  turned  over  or  used  once 
for  each  unit  of  output. 

The  contractor  bases  his  profit  on  costs  of  logging,  exclusive 
of  stumpage. 

Let  Lc  =  logging  costs. 

Me  =  milling  costs. 

.    f  LD  for  logging, 
D  =  depreciation  costs  {  .,_  ,        .„. 

\MD  for  milling. 

5  =  sale  value  of  lumber  or  of  logs. 

P  =  profit. 
Ym  =  stumpage  value  of   1000  board  feet  of 

manufactured  lumber. 
q%  =  legitimate  profit. 

Then  P  =  q%  (Lc  +  D}. 

Ym  =  S-(Lc  +  D}-  q%  (Lc 


STUMPAGE  VALUES  183 

That  is,  if  the  price  for  logs  is  taken  as  the  basis  of  prices, 
and  the  logger  computes  his  requisite  profit  roughly  as  a  per 
cent  of  average  logging  costs,  stumpage  value  is  the  residue 
after  subtracting  costs  and  profit  from  sale  prices. 

In  the  same  way,  milling  costs  and  profit  may  be  subtracted, 
and  (Method  A) 

Ym=S-(Lc  +  Mc  +  D}-q%(Lc  +  Mc  +  D}.          (R) 

Should  milling  require  a  different  profit  from  logging,  these 
costs  and  profits  may  be  separated,  using  r  per  cent  for  profit 
in  milling. 

Ym  =  S  -  (Me  +  MD  +  Lc  +  LD}-r%  (Me  +  MD) 

-q%(Lc  +  LD).  (RO 

The  computation  of  profits  as  a  per  cent  of  operating  costs, 
if  based  on  the  results  of  individual  operations,  would  place  a 
premium  on  extravagance.  But  when  gauged  by  average  costs 
of  well-conducted  operations  of  similar  size,  and  applied  in  deter- 
mining appraisals  in  advance  of  cutting,  no  such  objection  can 
be  urged. 

Method  B  assumes  that  stumpage  is  a  part  of  the  total 
operating  costs,  and  that  the  money  invested  in  it  is  entitled 
to  share  in  the  profit.  By  thus  adding  stumpage  to  the  sum 
of  the  other  expenses,  the  total  of  costs  plus  profit  equals  gross 
income,  or  sale  value.  Profit  thus  becomes  a  fixed  per  cent 
of  this  sale  value,  and  is  independent  of  operating  costs.  Any 
increase  in  operating  expense  of  logging  is  subtracted  from  cost 
of  stumpage,  and  vice  versa. 

The  formula  is: 

Ym  =  S  -  (Lc  +  Me  +  D)  -  q%  (Lc  +  Me  +  D  +  Fm), 
which  reduces  to 

Ym  =       f*       -(Lc  +  Mc  +  D).  (R.) 

I  T  (l/o 

This  formula  was  formerly  advocated  by  the  Forest  Service 
for  use  in  small  sales  where  but  little  capital  is  invested,  but  has 
been  set  aside  in  favor  of  Method  A.  The  profit  q%  should  be 
exclusive  of  a  salary  of  $1200  to  $1500  for  the  operator  (§34). 


184  FOREST  VALUATION 

Method  C  is  to  share  the  profit  or  margin  between  the  owner 
of  stumpage  and  the  operator.  Such  a  plan  requires  complete 
confidence  in  the  integrity  of  the  operator  or  a  right  to  inspect 
his  books,  and  is  not  generally  practiced,  though  one  of  the  most 
equitable  of  methods. 

It  is  the  only  one  of  the  three  methods  proposed  above, 
which  can  be  based  on  the  actual  costs  of  a  given  operation, 
with  safety  to  both  parties.  Letting  q  per  cent  equal  the  per 
cent  of  net  income  taken  for  stumpage  value,  the  formula  is 

Ym  =  q%\S  -  (Lc  +  Mc  +  D}\.  (Rs) 

In  the  following  diagram  the  basis  and  results  of  these  three 
methods  is  shown,  and  the  effect  of  an  increase  of  operating 
costs  upon  profits  and  stumpage  values. 

DIAGRAM  III 

COMPARISON  OF  COSTS,  PROFITS  AND  STUMPAGE  VALUE  BY  OVERTURN  METHODS 

Sale  Value  17.00 

Method  A 

Profit  20  H  of  Costs 

Costs  11.00  |      Stumpage  3.45     I     Profit  2.55    I 

Costs  13.00  |Si"4™'"Se|    Profit  2.5S~| 

Profit  15  %  of  Sale  Value 

Costs  11.00  1       Profit  3.00       I   Stumpage  SjHO  I 

Method  C 1 1 1 1  s.:miaM 

I  Costs  13.00  I  Profit  2.00 1    "jy    | 

Profit  50  *  of  Net  Income 

Operating  costs,  profits  and  stumpage  value  based  on  i  M  board  feet  of  lumber, 
scaled  in  the  log. 

178.  The  Investment  Basis  for  Profits.  —  Although  profit 
may  be  expressed  in'  terms  of  per  cent  of  cost,  or  of  sale  value 
for  a  unit  of  product,  it  can  be  correctly  gauged  only  as  a  return 
on  invested  capital  in  which  is  included  the  enterpriser's  gain 
(§§32,  33).  The  knowledge  that  a  profit  of  $i  per  thousand  feet 
has  been  earned  does  not  suffice  as  a  basis  for  dividends.  The 
reward  for  personal  services,  which  is  so  large  an  element  in  small 
undertakings,  disappears  with  large  enterprises,  and  net  income 


Costs  11.00 

Profit  2.20 

Stumpage  3.80       | 

costs  13.00                                                   1  Profit  2.60  |s^;8pasej 

STUMPAGE  VALUES  185 

or  profits  must  be  converted  into  annual  dividends  earned  on 
invested  capital. 

The  capital  upon  which  this  income  is  earned  is  the  entire 
amount  of  fixed  and  working  capital  employed  in  the  business, 
including  that  which  is  borrowed.  It  is  of  no  significance  that 
working  capital  is  turned  over  several  times  in  a  season,  as  is 
done  in  railroad  logging,  except  as  it  increases  the  total  net 
income  which  is  the  product  of  the  profit  per  thousand  feet 
multiplied  by  the  year's  output.  This  income  is  not  the  product 
solely  of  the  working  capital,  but  of  the  total  investment. 

Interest  on  borrowed  capital  is  paid  out  of  this  net  income, 
and  it  is  immaterial  whether  the  capital  entitled  to  share  in 
the  income  is  taken  as  the  entire  investment,  or  as  the  portion 
owned  by  the  proprietors,  excepting  that  the  latter  are  entitled 
to  a  larger  rate  of  profit  in  proportion  to  the  lessening  of  their  per 
cent  of  total  capital  and  corresponding  increase  of  risk  (§32). 
In  stumpage  appraisals  it  is  advisable  to  compute  the  profit  on 
the  total  investment,  thus  eliminating  the  purely  personal  ele- 
ment as  to  what  proportion  of  the  capital  is  borrowed. 

It  must  be  self-evident  that  interest  is  not  a  "cost"  in  stump- 
age  appraisals,  but  it  may  be  so  regarded  without  harm,  pro- 
vided it  is  not  added  to  operating  costs  in  Methods  A,  B  and  C 
(§  I77)>  and  is  subtracted  from  income  allowed  by  the  investment 
method.  To  permit  profits  to  be  earned  on  income  represented 
by  interest  on  owner's  capital,  results  in  serious  inflation  of 
profits  and  resultant  heavy  losses  in  stumpage  values  (§42). 

The  main  difficulty  in  computing  profits  in  the  form  of  a 
return  on  the  average  annual  investment  arises  from  the  ele- 
ment of  depreciation,  and  its  effect  in  reducing  the  capital 
invested  year  by  year. 

It  is  possible  to  earn  annually  about  the  same  net  surplus, 
available  for  depreciation  and  profits.  To  base  the  amount 
of  these  profits  upon  the  maximum  investment,  which  occurs 
normally  in  the  first  or  earlier  years,  results  in  a  steadily  in- 
creased rate  of  profit  on  the  capital  remaining  invested  in  sub- 
sequent years,  and  an  average  rate  considerably  greater  than 
intended,  with  corresponding  loss  in  stumpage  value. 


1 86  FOREST  VALUATION 

By  the  use  of  either  of  the  formulae  given  in  Article  175,  Method 
D  (P3,  P4),  a  fixed  rate  of  profit  may  be  found,  which  will  apply 
to  the  residual  capital  actually  invested  annually.  This  is 
accomplished  through  the  increasing  payments  for  depreciation. 
The  sum  of  interest  and  depreciation,  or  Z,  calls  for  equal  income 
annually.  This  conforms  with  the  financial  conditions  which  can 
normally  be  secured  in  lumbering.  To  the  owners,  it  makes 
very  little  actual  difference  whether  their  annual  income  is 
termed  dividends  or  depreciation.  They  expect  to  allow  the 
larger  portion  of  their  capital  to  remain  invested  throughout 
the  life  of  the  enterprise,  and  this  result  is  accomplished  by 
increasing  depreciation  from  small  beginnings.  Apparently, 
there  is  no  valid  objection  to  the  adoption  of  this  method  of 
determining  the  average  per  cent  of  profit  to  be  allowed  on 
invested  capital. 

Should  the  method  of  allowing  equal  annual  amounts  for 
depreciation  be  adopted  (§  175,  Method  B)  the  average  amount 
of  capital  invested  during  the  prospective  life  of  the  enterprise 
must  be  determined.  The  investment  for  each  year  is  taken 
at  the  beginning  of  the  year.  The  average  for  the  period  is  then 
equal  to  the  residual  or  final  investment  (W)  plus  one-half  the 
total  depreciation,  plus  one-half  the  annual  depreciation.  For 
an  investment  of  $20,000,  with  a  residual  value  of  $10,000,  over 
a  period  of  five  years,  the  values  at  the  beginning  of  each  year  are 

First  year $20,000 

Second  year 18,000 

Third  year 16,000 

Fourth  year 14,000 

Fifth  year 12,000 

Average  investment $16,000 

which  equals 

Residual  investment $10,000 

One-half  total  depreciation 5,ooo 

One-half  annual  depreciation 1,000 

Average  investment $16,000 


STUMPAGE  VALUES  187 

This  amount  would  be  taken  as  the  basis  for  computing  the 
per  cent  of  annual  profit  to  be  allowed. 

179.  Overrun.  —  When  the  amount  and  per  cent  of  profit 
have  been  determined,  the  remainder,  or  stumpage  value,  is  a 
definite  proportion  or  per  cent  of  the  sale  value  of  the  manu- 
factured products,  and  equals  a  stated  price  per  thousand 
board  feet.  Should  stumpage  appraisal  indicate  a  value  equal- 
ling 20  per  cent  of  the  wholesale  price  or  mill  price  of  lumber 
worth  $20  per  thousand,  the  price  of  stumpage  will  be  $4  per 
thousand  feet  of  sawed  lumber. 

But  this  does  not  indicate  that  the  true  price  of  stumpage 
is  $4.  It  is  probably  considerably  more.  The  contents  of 
logs,  and  not  the  measured  products,  is  the  basis  of  payment, 
not  only  when  the  timber  is  bought  on  the  stump,  but  when  it 
is  paid  for  after  being  felled  and  measured. 

Only  in  case  the  logs  are  measured  by  a  rule  which  will  give 
the  actual  sawed  contents,  will  the  appraised  stumpage  value 
per  thousand  feet  be  the  same  when  measured  by  log  scale 
and  by  sawed  contents.  All  log  scales  in  extensive  commercial 
use  give  less  than  the  contents  ordinarily  sawed  from  logs,  and 
this  discrepancy  increases  as  utilization  becomes  closer.  The 
excess  of  manufactured  lumber  over  the  contents  measured  by 
the  log  scale  is  termed  overrun. 

With  certain  log  rules,  notably  the  Doyle  and  Doyle-Scribner, 
this  excess  amounts  to  25  per  cent  and  over,  and  increases  with 
small  timber. 

Should  the  overrun  be  25  per  cent,  it  indicates  that  for  timber 
worth  $4  per  thousand,  each  thousand  feet  log  scale  produces 
1.25  thousand  feet  of  lumber.     The  value  of  the  stumpage  is 
therefore  1.25  X  $4,  or  $5  per  thousand. 
If 

Ym  =  stumpage  value  per  thousand  feet  of  sawed  lumber, 
s  =  per  cent  of  overrun  per  thousand  feet  of  log  scale, 
F  =  resulting  stumpage  value  per  thousand  feet  log  scale, 

then 

F  -  Ym  X  i.o5. 


1 88  FOREST  VALUATION 

180.  Stumpage  Values  for  Different  Species  in  Mixed  Stands. 
—  In  a  mixed  stand  containing  two  or  more  species,  the  sale 
value  of  the  products  of  these  species  usually  differs  considerably. 
Often  only  one  valuable  species  will  be  removed  from  a  mixed 
stand.  As  values  increase,  other  species  become  profitable,  and 
finally,  all  may  be  taken. 

At  a  point  just  before  the  inferior  species  become  sufficiently 
valuable  to  be  logged,  the  operator  is  under  the  necessity  of  con- 
structing his  transportation  system,  and  incurring  his  entire 
cost  for  equipment  and  overhead  expenses,  in  order  to  log  a 
portion  of  the  stand,  thus  moving  a  smaller  volume  of  lumber, 
at  relatively  greater  expense  per  unit. 

Assuming  that  the  total  costs,  including  depreciation,  amount 
to  $12  per  thousand  board  feet,  and  the  most  valuable  species 
is  worth  $20,  the  margin  for  profit  and  stumpage  is  $8.  A 
species  worth  but  $12  on  the  market  could  apparently  not  be 
marketed  at  all.  But  there  is  very  little  additional  investment 
involved  in  logging  this  second  species.  By  doing  so,  the  total 
average  cost  of  logging  may  be  reduced,  by  lessening  the  trans- 
portation expense  per  unit,  the  average  of  overhead  charges, 
and  the  depreciation,  to  $10  per  thousand  feet  for  the  entire 
operation.  This  adds  a  profit  of  $2  to  the  more  valuable  species, 
and  leaves  a  margin  of  $2  for  the  inferior  one,  for  profit  and 
stumpage. 

But  such  a  cost  distribution  is  unfair  to  the  inferior  species, 
since  the  operation  does  not  depend  on  its  presence  and  the 
capital  expenditures  must  be  incurred  without  its  inclusion. 
It  has  been  suggested  that  the  more  valuable  species  or  group 
be  made  to  bear  both  the  entire  cost  of  depreciation,  which 
represents  the  capital  expenditures,  and  the  overhead  charges. 
The  inferior  group  is  left  to  bear  merely  its  proportion  of  oper- 
ating costs.  This  plan  is  rather  crude  where  there  are  several 
species,  all  of  different  values. 

The  following  method  is  quoted  verbatim  from  the  Manual 
of  Stumpage  Appraisals,  U.  S.  Forest  Service,  November,  1914. 
This  plan  offers  an  equitable  solution  of  the  problem. 

"  The  most  satisfactory  method  is  to  pro-rate  the  gross  annual 


STUMPAGE  VALUES 


I89 


depreciation  and  profit  over  the  difference  between  operating 
cost  and  selling  price,  for  each  species,  in  the  quantities  entering 
into  the  annual  cut. 

To  illustrate: 

A  yearly  cut  is  made  up  of  4  million  feet  of  sugar  pine,  3  mil- 
lion feet  of  yellow  pine,  and  2  million  feet  of  white  fir  (giving  a 
total  of  9  million  feet).*  The  margins  between  selling  prices  and 
costs  of  production,  exclusive  of  depreciation  and  profit,  are: 


Species. 

Selling  price. 

Operating  cost. 

Margin. 

$2O    OO 

$IO    OO 

Yellow  pine 

18  oo 

8  oo 

White  fir  

(16.00) 

(10.00) 

6.00 

The  total  net  value,  or  sum  of  the  margins  over  which  depre- 
ciation and  profit  may  be  pro-rated,  is  thus: 

Sugar  pine $10.00  X  4000  M  —  $40,000 

Yellow  pine 8.00  X  3000  M  =    24,000 

White  fir 6.00  X  2000 M  =    12,000 

Total $76,000 

The  annual  sum  of  depreciation  and  profit  (investment 
method)  which  must  be  paid  out  of  this  total  has  been  computed 

as  $34,200.    Hence  34'200  =  $0.45.    That  is,  every  dollar  of 
76,000 

margin  between  operating  costs  and  selling  price  must  pay 
45  cents  toward  profit  and  depreciation.  Put  in  quantitative 
terms,  by  species,  we  have  the  following  charges  per  M  feet  for 
depreciation  and  profit: 

Sugar  pine 10  X  $0.45  =  $4.50 

Yellow  pine 8  X    0.45  =    3.60 

White  fir 6  X    0.45  =    2.70 

By  this  method  inferior  species  which  yield  no  margin  between 
operating  costs  and  selling  price,  or  a  negative  margin,  but 
which  must  be  included  in  the  sale  for  silvicultural  reasons, 


*  The  bracketed  material  does  not  appear  in  the  original  quotation  and  has 
been  inserted  as  additional  explanation. 


190  FOREST  VALUATION 

are  automatically  relieved  of  profit  and  depreciation,  and  the 
charge  upon  the  other  timbers  for  these  items  proportionately 
increased. 

The  same  result  is  readily  obtained  on  a  thousand  foot  basis, 
using  the  per  cents  of  the  different  species  in  the  cut.  That 
is,  to  obtain  the  average  margin  (of  sale  value  above  operating 
costs),  multiply  the  margin  for  each  species  by  the  per  cent  of 
this  species  in  total  cost: 

45  per  cent  sugar  pine  at  $10.00 $4.50 

33  per  cent  yellow  pine  at  $8.00 2.64 

22  per  cent  white  fir  at  $6.00 1.32 

Total $8.46 

Depreciation  and  profit  per  M  feet  ( -^^ —  1          $3.80. 

V  9000  / 

Q       =  $.045,  to  be  taken  from  each  dollar  of  margin  for 

0.40 

these  items. 

This  method  of  adjusting  the  prices  of  the  more  and  less 
valuable  species  is  believed  to  accord  with  customary  business 
practice.  Volume  of  money  handled,  rather  than  quantity 
of  this  or  that  product,  is  the  usual  basis  for  figuring  carrying 
charges,  depreciation  and  returns.  In  logging,  improvements 
are  frequently  constructed  primarily  to  take  out  certain  valua- 
ble species.  Inferior  timbers  may  be  cut  or  left  as  the  market 
warrants.  In  such  cases  operators  will  usually  cut  inferior 
species  if  a  profit  can  be  netted  over  bare  operating  costs,  figur- 
ing that  the  cost  of  improvements  is  borne  wholly  by  the  better 
stuff.  The  foregoing  is  believed  to  be  a  logical  and  rational 
application  of  this  principle." 

For  a  mixed  stand,  the  method  proposed  is,  therefore,  to  com- 
pute the  operating  costs  on  the  basis  of  the  total  amount  to 
be  logged,  including  inferior  species.  The  profit  and  deprecia- 
tion are  then  determined  as  a  lump  sum,  sufficient  to  pay  the 
required  per  cent  on  the  total  investments.  Finally,  this  sum 
is  charged  as  an  additional  "cost"  against  the  sale  value  pro- 
rated as  outlined  above  between  the  different  species.  The 


STUMPAGE  VALUES 


IQI 


remaining  margin  between  the  sale  value  of  a  species  and  these 
total  charges  is  its  appraised  stumpage  value. 

181.  Carrying  Charges  versus  Profits,  on  Stumpage.  —  In 
Chapter  X  (§  158),  it  was  demonstrated  that  a  forest  capable 
of  producing  annual  income  was  also  capable  of  paying  increased 
taxes,  for  the  reason  that  compound  interest  did  not  accumulate 
on  such  a  forest.  The  owner  may,  for  his  own  information, 
and  to  gauge  the  advisability  of  reinvesting  income,  compute 
the  interest  on  his  investment  for  the  interval  elapsing  between 
cost  and  the  income  directly  resulting  from  such  cost.  But  the 
total  cash  investment  in  the  business  does  not  increase  by  reason 
of  this  interest.  Neither  the  unearned  interest,  nor  the  actual 
cash  expenses  for  taxes  and  protection  serve  to  increase  the  capi- 
tal cost  of  stumpage,  as  long  as  sufficient  income  is  secured  each 
year  from  some  portion  of  the  forest  or  business  to  cancel  these 
costs. 

There  is  the  same  difference  between  tracts  of  mature  stumpage 
held  for  speculation  without  cutting,  and  tracts  on  which  an 
operation  is  conducted,  as  there  is  between  an  even-aged  and  an 
all-aged  forest,  Cases  A  and  C  (§  158).  The  first  case  is  paral- 
leled by  the  young  forest;  the  second,  by  the  forest  already 
capable  of  revenue.  For  timber,  or  that  portion  of  the  timber 
holdings  which  cannot  be  cut  for  from  20  to  40  years,  a  separate 
cost  account  based  on  economic  factors  (§  106)  would  show  iden- 
tical costs,  whether  or  not  the  specific  stand  is  a  part  of  a  large 
holding  which  produces  annual  revenue,  or  is  part  of  a  specula- 
tive holding  producing  no  income.  But  there  is  an  enormous 
specific  difference  in  the  financial  status  of  the  owners  of  the 
respective  tracts,  which  has  an  important  bearing  on  the  problem 
of  carrying  charges  and  increased  stumpage  values. 

The  non-productive  speculative  holding  requires  an  increase 
in  stumpage  values  sufficient  to  ultimately  offset  all  annual 
expenses,  and  earn  compound  interest  on  the  entire  investment, 
up  to  the  year  when  cutting  begins,  in  order  to  show  a  profit 
sufficiently  large  to  include  an  enterpriser's  gam  (§  33). 

The  productive  holding,  which  is  being  operated,  and  is  pro- 
ducing annual  income  at  the  present  time,  will  under  certain 


192  FOREST  VALUATION 

conditions  continue  to  pay  a  profit  as  great  as  it  pays  now,  if 
stumpage  does  not  increase  in  value,  or,  rather,  if  the  margin  of 
prices  over  cost  of  operation  does  not  increase  in  per  cent  (§  187). 
Were  the  forest  itself  composed  of  stands  of  all  ages,  which 
are  cut  upon  reaching  maturity,  this  condition  would  actually 
occur,  and  advancing  prices  for  stumpage  would  simply  increase 
the  profits. 

The  conditions  confronting  the  holder  of  stumpage,  who  is 
also  an  operator,  partake  of  both  of  these  extremes  or  lie  between 
them.  The  total  investment  in  stumpage  is  not  maintained, 
except  through  extending  the  area  by  purchase,  but  diminishes 
constantly  by  cutting,  with  a  corresponding  lightening  of  the 
annual  carrying  charges,  and  a  reduction  of  the  capital  invest- 
ment (§175). 

It  is  hardly  to  be  expected  that  a  company  planning  extensive 
operations  over  a  long  period,  will  inaugurate  a  scheme  of  cut- 
ting so  comprehensive  that  they  will  be  enabled  to  earn  their 
carrying  charges  for  the  first  few  years,  and  at  the  same  time 
pay  dividends  on  the  total  capital  investment.  The  actual 
annual  outlay  may  absorb  every  cent  of  annual  income  for  a 
while.  When  interest  on  bonds  is  added  to  other  carrying 
charges  the  burden  in  the  earlier  years  is  still  heavier,  and  it 
may  require  additions  to  capital  to  meet  these  charges.  Some 
companies  owning  extensive  timber  properties  have  lost  this 
timber  by  foreclosure,  because  of  non-payment  of  interest  on 
bonds  through  inability  to  obtain  this  additional  capital. 

With  reduction  in  interest  on  bonds,  in  taxes  and  in  other 
expenses,  a  company  comes  sooner  or  later  to  a  condition  per- 
mitting of  the  payment  of  dividends.  Up  to  that  time,  it  might 
be  assumed  that  the  value  of  stumpage  must  increase,  in  order 
that  the  dividends  when  received  shall  be  large  enough  to  com- 
pensate for  their  absence  in  earlier  years.  From  then  on,  with 
both  the  annual  expenses  and  dividends  paid  from  the  annual 
net  income,  an  increase  in  stumpage  value  or  in  net  income 
means  a  corresponding  increase  in  surplus  and  dividend  rates. 
When  a  company  is  able,  by  operating,  to  secure  a  sufficient 
net  income  to  meet  all  expenses  and  pay  dividends  from  the 


STUMP  AGE  VALUES  193 

start,  stumpage  value  does  not  need  to  increase  beyond  the 
amount  needed  to  meet  any  increased  costs,  in  order  to  maintain 
the  dividend  rate.  Furthermore,  this  rate  is  certain  to  in- 
crease, on  account  of  reduced  carrying  charges,  even  if  the  value 
of  stumpage  remains  stationary. 

The  claim  that  the  value  of  stumpage  must  increase  at  a 
rate  sufficient  to  return  compound  interest  on  all  costs,  or  the 
result  will  be  financial  loss  or  bankruptcy,  must  therefore  be 
flatly  rejected  except  for  purely  speculative  holdings,  or  for 
operators  attempting  to  carry  far  larger  holdings  than  they 
can  take  care  of  with  their  own  capital.  An  owner  of  stumpage 
must  either  have  sufficient  capital  to  carry  all  charges  for  an 
indefinite  period,  or  he  must  operate  and  obtain  revenue  annu- 
ally. In  either  case,  if  he  expands  his  operations  by  borrow- 
ing on  the  security  of  the  timber,  he  must  conduct  such  a 
transaction  with  considerably  greater  caution  and  conserva- 
tism than  is  necessary  in  many  other  forms  of  business,  or 
he  may  lose  his  holdings.  For  a  concern  which  is  earning 
annual  dividends,  increased  costs,  especially  taxation,  is  the 
only  factor  which  will  necessitate  the  realization  of  higher  values 
in  order  to  maintain  profits.  Very  strong  combinations  of 
capital  holding  timberlands  and  operating,  may,  by  a  policy 
of  cutting  calculated  to  cancel  carrying  charges,  put  themselves 
annually  in  a  better  financial  condition,  until,  after  the  period 
of  pressure  and  over-production  has  passed,  they  will  reap 
relatively  large  profits,  representing  more  than  average  divi- 
dends on  outstanding  capital  investments. 

This  distinction  between  the  separation  of  a  business  into 
parcels,  and  the  treatment  of  the  business  as  a  unit,  is  recog- 
nized by  the  U.  S.  Commissioner  of  Internal  Revenue  in  inter- 
preting the  income  tax  law  as  applied  to  corporations  dealing  in 
timberlands.  A  cost  account  is  to  be  kept  for  each  parcel  of 
land  as  the  basis  for  determining  net  income  (§25),  and  on  sale 
of  this  parcel  the  value  received  can  be  reduced  by  the  amount 
of  the  original  cost  of  the  parcel,  but  cannot  be  absorbed  by 
applying  it  to  cancel  capital  cost  for  any  other  parcel.  On  the 
other  hand,  net  income  is  treated  as  applying,  not  to  the  parcel, 


194  FOREST  VALUATION 

but  to  the  entire  business  of  the  concern.  If  actual  cash  ex- 
penses in  any  year  exceed  actual  income,  such  expenses  can  be 
added  to  capital  cost,  and  pro-rated  among  the  parcels.  The 
net  income,  after  subtracting  capital  cost  of  the  parcel  sold, 
may  be  used,  as  far  as  needed,  to  cancel  actual  outlay  on  the 
entire  tract  for  the  year,  the  surplus  income  remaining  after 
this  total  expense  is  met  being  the  only  portion  subject  to  the 
federal  income  tax. 


CHAPTER  XII 
FUTURE   VALUE   OF   FOREST  PRODUCTS 

182.  Factors  Affecting  Future  Value.  —  Since  the  value  of 
forest  property  is  derived  from  income,  an  appraisal  of  the  future 
value  of  forest  products  must  precede  that  of  the  property 
itself  and  forms  the  basis  for  this  appraisal.     The  examiner 
must  base  his  conclusions,  first,  on  the  character  and  present 
condition  of  the  property  and  its  probable  productiveness,  and 
second,  upon  the  factors  which  will  affect  the  value  of  the  prod- 
ucts secured.    The  elements  demanding  consideration  are: 

The  Stand, 

Growth  in  volume. 
Improvement  in  quality  of  products. 
Deterioration  of  standing  timber. 
Closeness  of  utilization. 

Price  Levels. 

General  price  changes. 

Changes  in  prices  for  forest  products. 

Effects  of  substitutes  for  wood. 

Future  Operating  Costs. 
Local  Factors. 

Future  transportation  facilities. 

Industries  and  markets. 

Future  supply  of  timber. 

183.  The  Stand;    Growth  in  Volume.  —  The  future  growth 
in  volume  of  a  stand  of  timber  may  be  predicted  for  short  periods 
by  measurements  of  past  growth  on  average  trees.     For  periods 
exceeding  a  decade  this  method  becomes  unreliable  by  reason 
of  the  progressive  loss  in  numbers  and  altered  rate  of  growth 
of  single  trees  which  takes  place  in  all  stands  as  they  increase 


196  FOREST  VALUATION 

in  age.  Yield  tables  attempt  to  state  the  actual  results  in  volume 
per  acre,  produced  by  stands  at  different  ages.  When  applied 
to  young  timber  growing  upon  sites  of  the  same  quality,  and  of 
approximately  equal  density  or  degree  of  stocking,  the  growth 
and  future  volume  of  such  stands  is  predicted  with  sufficient 
accuracy.  For  scattered  timber  or  poorly  stocked  stands,  a 
reducing  factor  is  required  to  prevent  over-estimates.  Methods 
of  studying  and  predicting  yields  per  acre  form  part  of  the 
subject  of  forest  mensuration.  Tables  of  growth  and  yield 
are  published  by  the  U.  S.  Forest  Service  and  in  various  state 
bulletins,  but  are  still  very  deficient  in  number  and  reliability. 

184.  The  Stand;    Improvement  in  Quality  of  Products.— 
Volume  alone  does  not  measure  the  increase  in  value  of  a  stand 
of  timber.     As  the  trees  become  larger,  the  quality  of  the  prod- 
ucts which  may  be  cut  increases,  for  two  reasons,     The  lower 
branches  on  young  trees  form  knots  as  long  as  they  remain 
attached,  either  alive  or  dead.     After  the  branch  falls  and  the 
scar  heals,  the  wood  laid  on  is  free  from  knots,  or  clear,  and 
produces   the  most   valuable   grades.     The   slabs   contain   the 
greatest  per  cent  of  clear  lumber  of  any  portion  of  the  tree,  and 
old  trees  contain  enormously  greater  per  cents  of   high-grade 
products  than  young  timber.     The  second  factor  of  increase 
in  quality  is  due  to  the  larger  sizes  which  can  be  cut  from  older 
trees.     Both  in  length  and  breadth,  higher  prices  are  paid -for 
increased  dimensions. 

Both  volume  and  quality  increase  the  value  per  acre  entirely 
independent  of  changes  in  prices  due  to  economic  conditions 
outside  the  stand. 

185.  Deterioration    of    Standing    Timber.  —  After    timber 
reaches  a  certain  age  and  condition,  the  stand  as  a  whole  ceases 
to  increase  in  volume,  and  at  a  much  later  period  it  begins  to 
diminish  in  quality  as  well.     The  trees  continue  to  grow  as 
long  as  they  live,  but  the  total  growth  of  the  stand  is  offset  by 
the  loss  of  trees  through  windfall,  insects  and  disease. 

The  remaining  trees  are  putting  on  clear  lumber,  but  in  old 
stands,  decay  caused  by  fungi  becomes  increasingly  prevalent, 
and  finally  offsets  this  increase  in  quality. 


FUTURE  VALUE  OF  FOREST  PRODUCTS        197 

In  Washington  it  was  shown  that  Douglas  fir  stands  yielding 
65  thousand  board  feet  per  acre  at  their  maximum,  deteriorate 
to  25  thousand  feet  in  100  years,  an  average  annual  loss  of  400 
board  feet  in  volume  alone.  Similar  losses  are  occurring  in  all 
over-mature  stands  regardless  of  species  or  locality. 

186.  Closeness  of  Utilization.  —  Present  volume  of  standing 
timber  is  expressed  in  terms  of  the  quantities  actually  utilized 
rather  than  the  cubic  contents  of  the  stand.     A  future  increase 
in  the  closeness  of  utilization  thus  has  the  effect  of  increasing 
the  apparent  volume  of  the  stand.     Its  effect  on  future  income 
is  of  similar  importance  to  that  of  actual  growth  in  volume  and 
quality.     In  regions  where  markets  for  the  poorer  grades  are 
uncertain,  these  grades  are  seldom  manufactured  or  included  in 
an  estimate  (§  172).     The  future  increase  in  merchantable  volume 
from  closer  utilization  alone  is  a  large  factor. 

In  addition  to  the  gain  in  volume  per  tree  the  total  merchant- 
able yield  of  the  stand  is  increased  by  removal  of  smaller  trees 
and  of  species  formerly  unprofitable. 

187.  Price  Levels;  General  Price  Changes. — General  changes 
in  prices,  caused  by  fluctuations  in  the  value  of  money  (§3) 
would  raise  the  cost  of  logging  and  milling  in  equal  ratio  to 
the  value  of  the  product.    When  the  ratio  of  profit  to  costs 
remains  the  same,  stumpage  values  will  increase,  at  the  same  rate 
or  per  cent  as  will  prices  for  lumber.     For  instance,  should 
lumber,  now  worth  $15,  increase  to  $20,  or  33^  per  cent,  stump- 
age  value  worth  at  present  $3  should  then  be  worth  $4.     In 
this  case  costs  might  be  assumed  originally  as  $9.60  and  profit 
$2.40,  or  25  per  cent  of  cost.    An  advance  of  33^  per  cent  in 
prices  of  supplies  and  labor  would  bring  costs  up  to  $12.80,  and 
25  per  cent  profit  would  equal  $3.20,  or  a  total  of  $16,  thus 
leaving  the  required  margin  of  $4  for  stumpage. 

Prof.  Irving  Fisher  predicts  an  average  annual  increase  in 
general  prices  of  2  per  cent  per  year  for  the  next  fifteen  years.* 

188.  Price  Levels ;   Changes  in  Prices  of  Forest  Products.  — 
The  prices  for  a  given  product  will  depart  from  the  average 

*  American  Economic  Review,  Sept.,  1912,  Vol.  II,  No.  3,  p.  553.  Managing  Edi- 
tor, Prof.  Davis  R.  Dewey,  491  Boylston  St.,  Boston. 


198  FOREST  VALUATION 

price  level  when  the  demand  for  the  specific  goods  increases 
relatively  faster  than  the  supply.  Both  demand  and  supply  may 
be  increasing,  or  both  decreasing,  or  demand  may  increase  while 
supply  diminishes.  In  any  case,  the  effect  on  prices  is  gauged 
by  the  difference  rather  than  by  the  direction  of  these  forces. 

When  population  is  increasing,  while  the  area  occupied  by 
timber  tends  to  decrease,  the  maintenance  of  the  same  per  capita 
rate  of  consumption  for  timber  causes  demand  to  progressively 
outrun  supply;  and  this  factor  has  resulted  in  the  past  two 
decades  in  an  increase  in  lumber  prices  approximately  twice 
as  rapid  as  the  movement  of  prices  in  general.  This  increase 
has  had  a  pronounced  effect  on  stumpage  values.  Instead  of 
increasing  by  the  same  per  cent  as  the  price  of  lumber,  the  value 
of  stumpage  tends  to  absorb  the  entire  surplus  not  taken  by 
increased  costs  (§  170).  The  profits  of  the  logger  and  millman 
tend  to  maintain  a  fairly  constant  ratio  to  cost  of  operation, 
except  where,  by  retarding  the  advance  in  stumpage  values, 
they  are  able  to  appropriate  a  larger  share  of  this  increase. 
In  the  above  illustration,  the  price  of  lumber  can  be  assumed  to 
have  increased  from  $15  to  $25,  or  66|  per  cent,  while  general 
prices  and  the  cost  of  logging  advance  but  33^  per  cent.  If  a 
profit  of  25  per  cent  on  operating  costs  is  still  considered  satis- 
factory, these  costs  advance  only  to  $16,  and  the  margin  of  value 
for  stumpage  becomes  $9,  an  increase  of  200  per  cent. 

In  regions  where  timber  was  formerly  barely  accessible  (§  1 74) 
this  increase  in  value  sometimes  amounts  to  several  hundred 
per  cent  on  cost.  Stumpage  in  general  doubled  and  trebled 
in  value  in  most  regions  of  large  supplies  in  the  decade  of  1898- 
1908. 

189.  Effects  of  Substitutes  on  Wood  Prices.  —  Increasing 
prices  for  lumber  and  other  wood  products  act  in  two  ways 
to  diminish  consumption  of  wood.  Less  wood  is  used  merely 
because  it  costs  more  and  the  enterprises  depending  on  wood 
are  curtailed;  and  substitutes  appear,  made  possible  by  this 
same  increase  in  price. 

The  extent  to  which  substitutes  will  succeed  in  permanently 
displacing  wood  as  a  raw  material  depends  upon  three  factors: 


FUTURE  VALUE  OF  FOREST  PRODUCTS        199 

The  relative  adaptability  of  wood  and  its  substitutes  for 

the  services  demanded. 

The  relative  cost,  measured  in  first  cost  of  raw  material, 
labor  of  construction  and  durability  or  cost  of  deprecia- 
tion. 

The  habits  and  customs  of  consumers  as  influenced  by 
advertising  and  imitation. 

When  no  substitutes  can  be  found  which  will  give  the  kind 
of  service  demanded,  the  use  of  wood  will  be  continued,  at 
constantly  advancing  prices,  until  the  supply  is  completely 
exhausted,  when  the  need  for  which  this  wood  was  used  will 
remain  unsatisfied.  But  ordinarily,  high  prices  will  force  the 
use  of  some  substitute  which,  while  not  so  satisfactory,  is  so 
much  cheaper  that  it  is  accepted. 

Formerly  wood  was  used  for  many  purposes  because  it  was 
cheaper  than  substitutes.  Board  fences  and  sidewalks  have 
been  replaced  by  wire  and  cement,  since  the  combined  cost  of 
labor,  material  and  depreciation  is  less  for  the  latter  materials 
and  they  give  better  satisfaction. 

Wood  for  buildings  .has  until  recently  been  much  cheaper 
than  brick  or  stone,  there  being  a  saving  in  labor  and  material. 
Old,  well-constructed  wooden  houses  depreciated  slowly.  At 
present  it  is  still  cheaper  to  build  wooden  houses,  but  there 
is  less  difference  in  the  cost  of  materials,  while  the  poor  quality 
of  much  of  the  lumber  used  increases  depreciation  in  favor  of 
brick,  cement  or  stone.  A  further  element  of  cost  is  the  insur- 
ance of  wooden  buildings  demanded  by  the  extra  fire  risk. 

The  use  of  wood  for  boxes  and  crates  has  been  considerably 
lessened  by  substitutes  in  the  form  of  fibre  and  cardboard, 
which  are  cheaper  and  fully  as  satisfactory  for  many  purposes. 
Shingles  have  been  extensively  replaced  by  patent  roofing  which 
is  cheaper  in  both  labor  and  material,  although  possibly  not 
as  durable. 

The  effect  of  advertising  and  habit  is  especially  noticeable  in 
the  last  two  instances.  Manufacturers  of  patent  roofing  and 
of  cheap  boxes  have  expended  large  sums  to  capture  the  trade 
and  educate  consumers  into  using  their  products.  Such  changes 


200  FOREST  VALUATION 

are  made  with  reluctance  and  suspicion,  but  once  undertaken, 
the  imitative  faculty,  which  plays  so  strong  a  part  in  human 
affairs,  may  cause  a  very  rapid  extension  of  the  substitution 
and  force  producers  of  lumber  to  fight  for  the  retention  of  trade 
formerly  theirs  by  right  of  original  possession. 

In  spite  of  the  inroads  which  substitutes  have  made  on 
consumption  of  wood  as  the  result  of  high  prices  and  trade  de- 
velopments, there  remain  many  uses  for  which  wood  is  so  pre- 
eminently adapted,  that  the  total  consumption  is  almost  certain 
to  increase  in  the  future  rather  than  to  diminish.  For  railroad 
ties,  the  resilience  or  elasticity  of  wood,  which  absorbs  the  shock 
of  traffic,  combined  with  the  small  labor  cost  of  track  repairing, 
and  increased  safety  of  travel,  when  compared  with  the  sub- 
stitutes so  far  employed,  make  it  certain  that  the  price  of  rail- 
road ties  will  be  much  higher  than  at  present  before  the  railroads 
discontinue  the  use  of  the  wooden  tie. 

A  still  more  striking  case  is  the  use  of  wood  for  paper  pulp. 
Formerly  confined  largely  to  spruce  and  poplar,  pulp  is  now 
made  from  many  hardwoods  and  from  southern  longleaf  pine. 
Paper  can  be  made  from  many  other  materials,  such  as  rags 
or  corn  stalks,  but  the  cost  of  assembling  sufficient  quantities 
at  the  mill  is  greatly  in  favor  of  wood. 

The  general  effect  of  substitutes  is  to  diminish  the  use  of 
cheap  grades  of  wood,  and  to  increase  the  supply  available  for 
more  important  uses.  This  tendency  is  illustrated  in  the  case 
of  fuel.  Wood  for  domestic  fuel  is  still  used  in  enormous  quan- 
tities, but  only  at  points  near  the  source  of  supply.  Its  bulk 
and  weight  prevent  its  transportation  by  freight  for  long  dis- 
tances to  large  centers  of  consumption.  It  is  probably  worth 
as  much,  if  not  more,  for  this  purpose  in  most  localities  than 
it  ever  was.  It  would  have  been  impossible  for  our  forests  to 
supply  enough  fuel  for  the  entire  demands  of  modern  industry. 
The  substitution  of  coal  has  relegated  wood  to  the  position  of 
a  luxury  for  the  fireplace  in  most  large  cities;  has  ruined  the 
markets  for  cordwood  formerly  existing  in  connection  with  cer- 
tain manufacturing  enterprises,  and  in  some  regions  near  such 
factories  has  caused  the  value  of  woodlands  to  decline.  Yet  the 


FUTURE  VALUE  OF  FOREST  PRODUCTS        2OI 

general  effect  of  this  substitution,  where  the  market  has  been 
spoiled  for  cordwood,  is  to  encourage  the  growth  of  timber  of 
larger  dimensions,  suitable  for  ties,  telegraph  poles  and  lumber, 
from  which  the  owner  may  realize  eventually  as  large  a  profit 
as  from, his  cordwood.  Substitutes  thus  tend  to  bring  about 
longer  rotations,  greater  diversity  of  wood  products,  higher 
values  per  acre,  and  increased  usefulness  of  each  acre  of  forest, 
and  do  not,  in  general,  interfere  seriously  or  permanently  with 
the  industry  of  wood  production.  Radical  changes  in  the  man- 
agement of  forests  may  become  necessary  by  these  economic 
changes  in  utilization  and  markets,  and  the  rate  of  interest 
earned  in  private  forestry  may  be  diminished  by  the  necessity 
of  longer  rotations  and  more  specialized  products.  New  uses 
for  wood  spring  up  to  take  the  place  of  former  demands  now 
obsolete. 

The  use  of  substitutes  will  undoubtedly  prevent  wood  prices 
from  rising  as  rapidly  as  in  the  decade  1898-1908  and  probably 
explains  in  some  measure  the  slower  increase  which  has  occurred 
since  that  date.  But  substitutes  will  never  do  away  with  the 
use  and  demand  for  wood,  nor  cause  the  average  value  of  wood 
products  and  timber  stumpage  to  be  lowered  to  any  appreciable 
extent.  Prices  are  still  far  below  the  level  established  in  Europe, 
and  it  is  reasonable  to  expect  that  these  prices  will  continue 
to  increase  slightly  faster  than  those  for  other  goods,  for  some 
time  to  come. 

190.  Future  Operating  Costs.  —  Future  costs  of  logging  and 
milling  will  increase  approximately  at  the  same  rate  as  general 
prices.  Added  to  this  are  the  special  factors  which  may  cause 
operating  costs  to  vary  from  this  general  trend. 

The  cost  of  labor  is  the  largest  item  in  logging.  Throughout 
northern  regions  the  effectiveness  of  woods  labor  is  rapidly  di- 
minishing. Old-time  American  lumberjacks  are  very  rare,  and  a 
large  part  of  the  work  is  performed  by  inexperienced  foreigners, 
or  shifting  labor  from  the  city  slums,  resulting  in  an  increased 
cost  considerably  greater  than  can  be  accounted  for  by  increased 
wages.  This  tendency  is  offset  by  improved  efficiency,  as 
operators  learn  from  experience  the  use  of  the  best  technique. 


202  FOREST  VALUATION 

The  recent  development  of  logging  engineering  as  a  profession 
on  the  Pacific  Coast  is  in  response  to  a  recognition  by  operators 
of  the  possibility  of  greater  efficiency  and  economy  in  trans- 
portation. 

Extraordinary  increases  in  cost,  if  general,  must  ultimately 
be  taken  from  the  value  of  stumpage.  In  the  same  way,  a  gen- 
eral reduction  of  costs,  even  if  due  solely  to  improved  methods 
and  greater  efficiency,  will  increase  the  value  of  stumpage. 

191.  Local  Factors :  Future  Transportation  Facilities.  — 
With  increasing  population,  transportation  facilities  are  certain 
to  improve.  Tracts  of  timber  of  considerable  extent  and  volume 
will  be  certainly  reached  in  time  by  the  construction  of  railroads 
or  other  special  means  of  transportation.  A  far  more  serious 
question  arises  as  to  the  permanence  of  such  facilities.  If  there 
is  not  sufficient  use  for  them  to  justify  their  continuous  main- 
tenance after  the  present  merchantable  stand  is  removed,  they 
will  be  abandoned.  The  rails  and  ties  are  removed,  the  flumes, 
bridges,  trestles  and  corduroy  rot  away,  the  grades  become  gul- 
lied and  the  roads  grow  up  to  brush.  To  remove  any  timber 
in  the  future  these  structures  must  be  replaced.  There  must 
be  a  sufficient  stand  of  second  growth  not  only  to  furnish  the 
material  for  reconstruction  but  to  warrant  the  expense  (§  98) . 
The  original  stand  of  virgin  timber  may  have  been  several  hun- 
dred years  old,  and  far  more  valuable  per  thousand  feet  than 
this  second  growth  (§  184).  There  are  many  districts  where  a 
second  operation  will  be  financially  impossible,  and  timber 
grown  after  logging  will  remain  inaccessible  unless  a  very  con- 
siderable increase  occurs  in  the  value  of  stumpage  in  general. 
This  condition  applies  to  mountainous  or  non-agricultural  re- 
gions. Elsewhere,  increasing  population  assures  a  future  market 
for  all  timber. 

A  similar  increase  in  average  transportation  costs  per  thousand 
board  feet  occurs  with  the  exhaustion  of  the  more  accessible 
bodies  of  virgin  timber.  This  tendency  was  for  a  long  period 
overcome  by  a  corresponding  expansion  of  the  size  of  operations, 
the  amount  of  capital  invested,  and  the  quantity  of  timber 
tributary  to  a  single  transportation  system.  The  old  days  of 


FUTURE  VALUE  OF  FOREST  PRODUCTS        203 

hand  logging,  short  drives  and  heavy  timber  were  succeeded 
by  large  operations,  which  tapped  reservoirs  of  timber  of  great 
extent,  and  distributed  the  costs  over  enough  stumpage  to  bring 
them  even  below  those  of  the  simpler  undertakings.  When 
this  increasing  cost  is  no  longer  offset  by  increased  volume  to  be 
transported,  it  at  once  depresses  stumpage  values.  This  means 
that  average  quoted  prices  for  stumpage  may  not  rise  as  rapidly 
as  lumber  prices,  because  the  later  quotations  are  for  stumpage 
differently  situated.  The  rise  in  values  occurs,  but  is  evident 
only  for  the  same  or  similar  timber. 

An  important  consideration  in  forest  production  is  the  pos- 
sibility of  substituting  the  cost  of  growing  trees  in  accessible 
situations,  for  the  cost  of  transportation  from  regions  much 
farther  from  markets.  As  accessible  timber  disappears,  the 
difference  in  stumpage  value  between  timber  easy  and  difficult 
to  obtain  will  become  larger  and  larger,  and  this  margin  of  value 
can  be  expended  upon  forest  production  on  accessible  sites. 

192.  Local  Factors:  Industries  and  Markets.  —  Transpor- 
tation charges  are  subtracted  from  income  in  arriving  at  stump- 
age  value.  It  follows  that  the  farther  from  the  mill  the  timber 
lies,  the  less  will  be  its  value.  In  the  manufacture  of  lumber, 
portable  mills  brought  to  the  timber  greatly  reduce  the  cost 
of  hauling  this  lumber  to  the  market  by  leaving  the  waste  from 
sawing  in  the  woods.  But  the  greatest  value  for  many  woods 
lies  in  their  use  for  special  products,  such  as  spools,  excelsior, 
boxes,  match  stock  and  other  specialties.  These  factories 
pay  larger  prices  for  stumpage  since  they  utilize  the  tree  far 
more  completely  and  obtain  much  greater  returns  on  a  given 
amount  of  wood.  Local  industries  of  this  character  must 
operate  continuously  in  order  to  be  profitable.  They  remain 
in  a  region  as  long  as  they  can  obtain  a  sufficient  supply  of  raw 
material.  The  reduction  of  the  supply  to  a  point  where  the 
mills  can  only  run  part  time,  or  must  suspend  operations  for 
several  years,  results  in  driving  out  these  industries.  The 
remaining  stumpage  must  then  be  marketed  at  more  distant 
points,  perhaps  for  a  less  intensive  use,  and  there  is  a  very  con- 
siderable loss  in  value. 


204  FOREST  VALUATION 

193.  Local  Factors :   Future  Supply  of  Timber.  —  From  the 
factors  discussed  in  Articles  191  and  192  it  is  apparent  that  the 
local  value  of  timber  stumpage  in  the  future  depends  largely 
upon  the  total  quantity  of  timber  produced  in  that  locality, 
and  the  continuity  of  the  supply.     If  virgin  timber  is  being 
appraised,  its  value  must  often  be  based  on  the  premise  that  it 
will  be  logged  at  the  time  the  remaining  stumpage  is  cut,  since 
it  is  worth  more  now  than  it  may  ever  be  again.     If  the  timber 
is  of  second  growth,  or  is  in  a  region  of  second  growth,  the  extent, 
average  age,  vigor  and  utility  of  this  second  growth  is  of  the 
greatest  importance  in  appraising  the  value  of  any  separate  par- 
cel or  tract.     Where  most  of  the  cut-over  areas  are  ravaged  by 
fire,  or  otherwise  rendered  worthless,  an  isolated  patch  of  repro- 
duction or  plantation  not  only  costs  more  to  protect,  but  its 
stumpage  value  is  permanently  less  in  such  a  region  than  if  it 
were  a  part  of  an  abundant  second  growth.     It  may  pay  better 
to  plant  trees  in  regions  where  natural  reforestation  is  abundant 
than  under  the  reverse  conditions.     By  following  out  this  argu- 
ment it  will  be  seen  that  extensive  operations  on  the  part  of 
states  or  the  national  government  to   protect   and   reproduce 
large  areas  of  forest  will  have  the  effect  of  raising  stumpage 
prices    for    those    private    owners    who    grow    trees    in    such 
localities. 

194.  The  Rate  of  Increase  in  Stumpage  Value.  —  By  care- 
fully weighing  both  general  tendencies  and  the  equally  important 
local  factors,  the  examiner  may  appraise  the  probable  stumpage 
value  of  timber  with  considerable  accuracy  for  a  period  of  10  to 
15  years  in  the  future.     Beyond  this  period,  so  many  unforeseen 
events  may  occur  to  affect  prices  that  only  a  semblance  of  accu- 
racy can  attach  to  such  appraisals.     One  of  two  suppositions 
can  be  made.     The  value  may  be  assumed  to  remain  constant 
beyond    a   certain  year.     The    tendencies    of   prices    and    the 
history  of  wood  consumption  justify  so   conservative  a  con- 
clusion. 

The  second  assumption  is  that  prices  will  continue  to  advance 
at  the  same  per  cent  as  in  the  past.  The  validity  of  this  con- 
clusion depends  upon  the  meaning  attached  to  the  phrase; 


FUTURE  VALUE  OF  FOREST  PRODUCTS 


205 


whether  simple  or  compound  interest  is  meant,  that  is,  whether 
the  original  value  or  the  increasing  value  is  the  basis  of  the 
annual  percentage.  Stumpage  as  a  residual  value  is  subject  to 
more  extensive  proportional  changes  than  the  price  of  timber 
products  which  causes  these  changes  (§  188).  Then,  while  prices 
and  stumpage  value  may  rise  at  a  rate  equal  to  simple  interest 
on  the  value  at  a  given  date,  the  rate  of  interest,  simple  or  com- 
pound which  this  rise  represents,  when  based  on  increased  prices 
or  values,  becomes  less  and  less. 

Table  V  illustrates  these  relations.  Should  stumpage  rise 
from  an  original  value  of  $5  per  thousand,  by  the  sum  of  $5 
every  10  years,  or  50  cents  per  year,  the  rate  of  increase  would 
be  equivalent  to  10  per  cent  simple  interest  annually  on  the 
original  value. 

TABLE  V 
RATE  OF  ANNUAL  INCREASE  IN  VALUE  OF  STUMPAGE 


Period, 
years. 

Value  of 
stumpage, 
dollars. 

Rate  of  simple 
interest  on 
original  value, 
per  cent. 

Rate  of  com- 
pound interest 
on  original 
value, 
per  cent. 

Rate  of  simple 
interest  on 
value  for  each 
decade, 
per  cent. 

Rate  of  com- 
pound interest  ; 
on  value  for 
each  decade, 
per  cent. 

o 

5  °° 

10 

10.00 

10 

7.2 

IO 

7-2 

20 

15.00 

IO 

5-6 

s 

4-1 

3° 

20.00 

IO 

4-7 

3-3 

2-9 

40 

25  .00 

IO 

4-i 

2-5 

2-3 

50 

30.00 

IO 

3.65 

2 

1.85 

Values  of  stumpage  are  more  apt  to  follow  the  law  of  increase 
set  forth  in  this  table  than  to  increase  continuously  at  a  fixed 
rate  of  compound  interest.  It  follows  that  as  prices  and  values 
advance,  the  rate  of  increase  must  fall.  By  first  predicting  the 
amount  of  the  increase,  or' the  rate  expressed  in  terms  of  simple 
interest  on  original  value,  the  rate  of  compound  interest  for 
these  values  may  be  computed  if  desired  (§  89,  Formula  XIV; 
see  also  §49). 

The  true  rate  of  increase  in  stumpage  value  depends  upon 
the  sum  of  increased  values  due  to  growth  in  volume,  improved 
quality,  closer  utilization  and  price  increment.  These  sources 


206  FOREST  VALUATION 

may  be  expressed  separately,  as  if  each  represented  a  rate  of 
interest,  as 

F0(i.oa)(i.o6)(i.oc)  =  Vi, 
which  is  slightly  greater  than 


In  ascertaining  the  values  of  the  factors  a,  b,  etc.,  for  a  period  of 
some  years,  these  values  must  either  be  taken  as  representing 
simple  interest,  or,  if  compounded,  the  rate  quoted  for  the 
entire  period  must  be  much  lower  than  the  probable  annual 
increase  in  the  earlier  years. 

195.  Increasing  Future  Values  as  a  Basis  of  Appraisals.  — 
As  set  forth  in  Article  139,  the  elements  of  increase  in  value 
inherent  in  the  character  and  condition  of  the  property  itself 
must  be  accepted  as  reliable  and  occurring  in  the  natural  course 
of  events,  and  will  be  recognized  in  appraisals  for  public  purposes, 
such  as  damage  suits  and  condemnation  proceedings.  These 
include  growth  and  quality  increment.  But  the  factors  of 
closer  utilization  and  rising  prices  depend  upon  outside  influ- 
ences shown  to  be  affected  by  a  complex  of  causes  and  therefore 
not  capable  of  reliable  diagnosis. 

The  acceptance  of  such  increased  prices  as  a  basis  of  appraisals 
must  be  determined  by  the  purpose  of  the  appraisal,  and  by 
the  evidence  on  which  the  conclusions  rest.  Reasonable  con- 
servatism is  required  in  appraisal  of  damages.  A  more  liberal 
construction  is  permitted  in  condemnation  proceedings.  In 
either  case,  evidences  to  prove  the  probability  of  rising  prices 
must  take  into  account  both  the  general  and  local  factors  dis- 
cussed in  this  chapter,  and  it  will  usually  be  found  advisable 
to  make  very  moderate  claims  on  this  score. 

As  a  basis  of  valuation  to  determine  a  tentative  sale  value, 
it  is  equally  necessary  to  treat  the  element  of  future  prices 
conservatively.  The  purchaser  is  entitled  to  this  source  of 
future  profits,  and  should  base  his  price  for  the  property  upon 
present  rather  than  future  prices  for  products.  As  tending 
merely  to  show  the  probable  amount  and  present  value  of  these 


FUTURE  VALUE  OF  FOREST  PRODUCTS        207 

profits,  for  the  information  of  the  owner,  no  objection  can  be 
urged  to  any  assumption  which  he  can  reasonably  justify. 

196.  Revision  of  Stumpage  Values  in  Long-term  Contracts.  — 
In  timber  sale  contracts,  where  timber  is  paid  for  at  time  of 
purchase,  the  owner  of  the  stumpage,  in  return  for  the  risks 
incidental  to  carrying  this  investment,  is  entitled  to  share  in 
the  increased  values  which  may  materialize  (§176).  For  periods 
of  less  than  five  years  this  factor  is  immaterial.  If  the  contract 
is  for  longer  periods,  at  a  fixed  price,  the  purchaser  is  usually 
willing  to  operate  at  a  loss  during  the  earlier  portion  of  the  term, 
in  expectation  of  realizing  increasing  profits  later  on.  In  this 
way  the  increase  may  be  shared  with  the  owner  even  on  the  basis 
of  a  fixed  contract  price.  Contractors  desire  certainty  in  the 
element  of  cost  of  raw  materials,  even  at  some  sacrifice  of  possible 
profits. 

The  ideal  arrangement  is  some  form  of  revision  at  stated 
intervals,  by  which  the  value  of  stumpage  is  readjusted  to 
changing  conditions.  Such  a  revision  may  be  based  on  a  reap- 
praisal. This  would  take  into  account  the  element  of  closer 
utilization,  as  well  as  advancing  prices.  The  factor  of  growth 
is  accounted  for  by  the  scale,  while  changes  in  quality  are  usually 
neglected,  but  can  be  considered  in  reappraisal.  This  method 
is  advocated  in  the  Forest  Service  for  regions  where  close  compe- 
tition exists  for  government  timber. 

A  second  plan  for  revision  confines  the  changes  to  the  single 
factor  of  prices  for  lumber,  neglecting  those  of  utilization  and 
quality.  The  point  to  be  determined  is  the  per  cent  of  increase 
in  lumber  prices  which  should  be  appropriated  by  stumpage. 
On  the  basis  that  timber  prices  have  advanced  in  the  past 
more  rapidly  than  costs,  the  Forest  Service  has  claimed  as  much 
as  75  per  cent  of  this  increase  for  stumpage.  Their  present 
basis  is  to  appropriate  50  per  cent  of  increased  prices  as  stumpage 
value.  Revision,  without  reappraisal,  is  undertaken  at  intervals 
of  five  years.  The  prices  of  lumber  accepted  as  a  basis  (§172) 
are  averaged  for  three  years  previous  to  revision. 


CHAPTER   XIII 
RISKS 

197.  Risks  versus  the  Rate  of  Interest  in  Forestry.  —  The 

risks  to  which  forest  property  is  exposed  tend  to  discourage 
the  investment  of  funds  in  forest  production,  in  the  same  manner 
that  similar  risks  restrain  investors  in  other  enterprises.  This 
tendency  is  expressed  by  an  increase  in  the  basic  rate  of  interest 
at  which  capital  will  seek  investment  in  forestry  (p  per  cent). 
A  high  rate  of  interest  is  the  expression  of  a  fear  entertained  for 
the  safety  of  the  principal.  The  use  of  such  a  rate  gives  very 
low  expectation  values  for  probable  future  income. 

When  the  per  cent  which  can  be  earned  by  forest  enterprises 
is  lower  than  the  rate  of  interest  demanded,  capital  is  presum- 
ably unwilling  to  invest  in  forestry  because  the  average  risk 
of  loss  exceeds  the  probable  income.  Should  individuals  still 
be  willing  to  undertake  forestry,  they  do  so  because  they  place 
a  lower  estimate  upon  this  risk  than  that  commonly  prevailing, 
or  expect  to  combat  it  by  effectual  preventive  measures;  hence 
their  individual  "rate  of  interest"  is  gauged  proportionally 
lower  and  indicates  possible  profit. 

198.  The  Character  of  Risks  in  Forestry.  —  Risks  may  be 
classed  as  physical,   moral  and  financial.     Physical  risks  are 
those  incurred  through  the  operation  of  the  forces  of  nature. 
In  case  of  fire,  the  physical  risk  is  greatly  increased  by  the  addi- 
tion of  a  moral  risk.     Moral  risks  are  those  arising  through 
possible  human  actions,  either  deliberate  or  accidental.     Finan- 
cial risks  include  both  physical  and  moral  elements,  since  all 
risks  are  measured  by  the  probable  financial  losses  that  may  be 
inflicted.     But  the  risk  of  loss  of  profits  exists  quite  independent 
of  these  other  factors,  and  is  influenced  by  changing  economic 
conditions,  such  as  demand,  prices,  future  taxation  and  any  other 

208 


RISKS  209 

element  which  serves  to  diminish  profits  below  the  expected 
amount. 

199.  The  Gauging  of  Risks.  —  There  are  two  elements  to  a 
risk:    the  hazard,  or  degree  of  probability  that  damage  will 
occur,  as  indicated  by  past  history  and  present  conditions;  and 
the  liability,  or  value  of  the  property  subject  to  damage.     The 
liability,    in   forest   investments,   is   measured   by   expectation 
value  for  partially  mature  stands;  but  for  plantations,  cost  is 
the  basis  considered,  and  extra  efforts  will  be  made  to  protect 
such  plantations  because  of  the  investment  which  they  represent. 
The  hazard  must  be  gauged,  during  the  growth  of  the  crop,  by 
the  increasing  or  decreasing  susceptibility  or  resistance  of  the 
trees  to  fire,  wind,  insects  and  fungi,  and  by  the  probability  of 
these  events  occurring,  through  prevalence  of  the  causes. 

When  the  liability  is  large,  and  the  hazard  is  extreme,  active 
preventive  measures  involving  considerable  expense  are  jus- 
tified. 

With  a  small  present  liability  and  extreme  hazard,  the  ques- 
tion arises  whether  protective  expenses  will  pay  for  themselves. 

When  liability  is  large,  but  the  hazard  negligible,  protective 
measures  may  involve  a  needless  expense,  and  diminish  profits 
and  value. 

With  small  present  liability,  and  negligible  hazard,  the  ex- 
penditure justified  for  forest  protection  is  still  further  reduced. 

The  financial  character  of  the  risk  thus  indicates  the  expense 
which  should  be  incurred  for  protection.  The  largest  expen- 
ditures are  justified  when  property  of  considerable  value  is  in 
great  danger  of  being  destroyed. 

200.  Physical   Risks :    Fire.  —  Fire  is   by  far  the   greatest 
risk  in  forest  production.     The  resistance  of  trees  to  fire  damage 
depends  on  the  character  of  the  bark,  which  differs  with  the 
species,    and  on  its  thickness,  which  increases  with  age  for  all 
species.     Sandy  soils  in  all  regions  are  far  more  subject  to  fire 
than  soils  which  retain  moisture.     In  many  localities  fires  burn 
annually  on  such  sites.     As  a  consequence,   the  tree  species 
which  inhabit  these  situations  have  developed  a  fire-resistant 
bark  which  often  renders  them  immune  to  the  effects  of  ordinary 


210  FOREST  VALUATION 

fires.  This  immunity  is  attained  at  an  early  age,  but  seldom 
covers  the  period  of  reproduction,  or  the  seedling  stage  of  growth. 

On  soils  and  in  localities  where  fires  burn  only  at  long  intervals, 
most  tree  species  are  very  susceptible  to  injury,  and,  as  the 
fires  which  do  occur  on  these  sites  are  unusually  severe,  practi- 
cally the  entire  stand  may  be  killed.  The  younger  the  stand,  the 
greater  the  per  cent  of  mortality  and  consequent  proportion  of 
value  destroyed. 

The  fire  hazard  is  largely  due  to  the  inflammable  character 
of  the  forest  floor.  The  entire  mass  of  accumulated  litter  and 
humus  will  burn  when  dry  enough.  Most  of  the  undergrowth 
is  also  extremely  inflammable.  Shade  thrown  by  a  dense  cover 
reduces  the  risk  by  preventing  extreme  desiccation,  and  keeping 
out  brush  and  grass.  Of  the  materials  forming  the  forest  floor 
and  undergrowth,  grass,  when  dry,  is  the  most  inflammable. 
Pine  needles  come  next,  while  hardwood  leaves  do  not  cause  a 
serious  blaze.  Humus  or  duff,  when  dry  enough  to  burn,  causes 
a  slow  and  very  destructive  ground  fire,  difficult  to  extinguish. 

The  hazard  is  reduced  by  atmospheric  moisture.  Except  on 
the  sandiest  soils,  belts  of 'heavy  rainfall  will  give  rise  to  rank 
vegetation.  These  are]  regions  of  slight  hazard.  Over  most  of 
the  forest  areas  in  this  country  droughts  occur  either  annually 
or  at  greater  intervals,  of  sufficient  severity  to  create  an  exces- 
sive fire  hazard. 

This  risk  is  enormously  increased  by  logging,  because  of  the 
great  increase  in  litter  and  slash  incidental  to  the  operations. 
As  the  liability  is  reduced  in  like  proportion,  the  temptation 
to  ignore  the  hazard  and  abandon  the  attempt  to  protect  the 
residual  forest  values  is  very  great. 

201.  Wind.  —  Wind  resistance  is  greatest  with  small  timber, 
and  becomes  less  with  increasing  bulk,  weight  and  age.  The 
form,  distribution  and  penetration  of  the  roots  of  different 
species  determine  their  resistance  to  wind-throw.  Shallow, 
rocky  soils,  or  those  underlaid  by  hardpan  or  water,  induce 
windfall.  Regions  subject  to  frequent  tornadoes  present  a 
wind  hazard  which  must  be  reckoned  with  in  planning  the 
sequence  of  logging  operations.  This  risk  is  excessive  only  for 


RISKS  2il 

mature  and  over-mature  timber,  and  is  a  serious  factor  in  opera- 
tions where  a  portion  of  the  stand  is  left  for  a  second  crop  or  as 
seed  trees.  If  all  parts  of  a  tract  are  accessible,  wind-thrown 
timber  can  be  marketed  without  loss,  provided  the  quantity 
thrown  does  not  exceed  the  capacity  of  the  operation  as  gauged 
by  the  length  of  time  the  down  trees  can  be  left  without  deterior- 
ation. 

202.  Insects.  —  Imported  insects  as,  for  example,  the  gypsy 
and  brown-tail  moths  are  far  more  dangerous  to  forests  than 
native   insects,   as  they   are  practically   without   any    natural 
parasites.     The  introduction  of  these  enemies  now  promises  to 
keep  the  gypsy  moth  in  check. 

Native  insects  occasionally  develop  possibilities  of  injury, 
and  may  destroy  great  areas  of  forest.  They  are  finally  checked 
by  disease  or  parasites.  The  worst  of  these  insects  are  the  bark- 
boring  beetles.  Defoliating  insects,  like  the  larch  sawfly  or 
spruce  bud  worm,  may  kill  timber  over  entire  regions.  The 
destruction  of  native  birds  explains  the  increase  of  certain 
forms  of  injurious  insects.  Woodpeckers  are  very  useful  in 
keeping  boring  larvae  under  control. 

203.  Fungous   Diseases.  —  The  only  conspicuous  instance  of 
widespread  destruction  of  an  American  species  due  to  fungous 
attacks  is  found  in  the  ravages  of  the  imported  disease  of  the 
chestnut,  Diaporthe  parasitica,  which  threatens  to  exterminate 
what  is  considered  the  most  important  commercial  hardwood 
over  wide  regions  east  of  the  Appalachians.     Great  damage  is 
done  to  the  heartwood  of  all  species  of  trees  by  fungi  which 
gain  entrance  through  wounds  or  knots.     These  fungi  do  not 
kill  the  trees  as  they  have  no  effect  on  the  living  tissue.     This 
damage  is  greatest  in  old  timber  and  is  not  a  serious  factor  in 
second  growth. 

204.  Climatic  Injuries.  —  Excessive  drought  in  rare  instances 
kills  many  trees  of  the  more  susceptible  species  in  exposed 
regions  or  localities.     Trees  unused  to  swampy  conditions  are 
killed  by  prolonged  flooding  of  the  roots. 

Minor  injuries  are  caused  by  breakage  in  sleet  storms  or  heavy 
snows,  permitting  fungi  to  enter.  Reproduction  is  especially 


212  FOREST  VALUATION 

sensitive   to   frost,   drought   and   excessive   moisture,  but  the 
young  trees  soon  become  hardy. 

205.  Injurious    Fumes.  —  The    physical    injury    caused   by 
fumes  is  due   to  human  activities.     The  fumes  from  copper 
smelters  will  sometimes  kill  timber  seventy-five  miles  from  the 
location  of  the  smelter.* 

206.  Moral   Risks:     Trespass.  —  Timber   products   are   fre- 
quently stolen,  but  the  theft  is  easily  discovered,  and  it  is  not 
difficult  to  identify  the  trespasser.     Losses  from  this  source  are 
the  result  of  neglect  of  the  property,  and  are  easily  eliminated  by 
proper  marking  and  posting  of  boundaries,  and  the  employment 
of  a  custodian.     The  expense  of  such  protection  is  serious  for 
small  tracts  whose  owners  reside  at  considerable  distances,  but  is 
immaterial  for  larger  holdings.     The  character  of  the  population 
and  ease  with  which  small  quantities  of  timber  can  be  transported 
determine  the  degree  of  hazard. 

Trespass  is  frequent  in  connection  with  logging  operations, 
where  only  a  portion  of  the  stand  is  to  be  cut,  or  where  the  logger 
attempts  to  enlarge  his  operation  at  the  expense  of  adjoining 
owners.  Reputable  firms  incur  considerable  expense  in  relo- 
cating boundaries  not  only  to  prevent  others  from  trespassing, 
but  to  avoid  accidental  encroachment  on  adjoining  lands  by 
their  own  employees. 

207.  Moral  Risks:    Fire.  —  Some  fires  are  started  by  light- 
ning, but  the  great  majority  are  due  to  human  agencies.     Most 
of  these  fires  are  caused  by  careless  or  unintentional  acts,  but 
in  some  regions  the  habit  of  burning  is  firmly  fixed,  and  occa- 
sionally fires  are  set  through  malice.     The  moral  risk  thus  in- 
curred is  so  great  in  some  southern  states  that  it  presents 
an  almost  insuperable  obstacle  to  forest  production.     In  other 
localities   this  risk   is  chiefly  due  to  avoidable   factors,   such 
as  railroad  operation,  and  yields   to  preventive  measures  and 
education. 

208.  Financial  Risks.  —  The  risk  of  excessive  future  taxa- 
tion is  discussed  in  Chapter  X.     Unless  this  risk  is  removed,  it 
will  prevent  the  practice  of  private  forestry  in  the  regions  affected. 

*  Deerlodge  National  Forest,  Anaconda,  Montana,  1912. 


RISKS  213 

The  financial  risk  is  in  reality  a  summary  of  the  factors 
enumerated  above  plus  the  economic  risk  of  failure  to 
secure  remunerative  prices  (Chapter  XII).  The  economic 
situation,  except  in  certain  inaccessible  localities,  is  so 
favorable  that  the  only  serious  risks  are  those  discussed  in 
this  chapter. 

209.  Control  of  Risks :  Insurance.  —  Insurance  against  losses 
follows  rather  than  precedes  other  measures  for  the  control  of 
risks.     When   the   risk  is  large,  and  the  probable   amount  of 
damage   uncertain,   the  premiums  will  be  prohibitively  high. 
At  the  present  time,  no  insurance  against  fire  is  in  force  on 
standing  timber  in  the  United  States,  and  no  companies  will 
accept   such   risks.    Lloyds  of  London   have  insured  a  large 
tract  of  timber  in  Canada.* 

The  unreliability  of  appraised  values  in  case  of  damage,  and 
the  great  variation  in  value  of  stumpage,  adds  to  the  difficulty 
of  such  insurance  projects.  Standing  timber  in  European  states 
is  widely  insured  at  low  rates.  Tornado  insurance  on  timber 
is  available  in  the  United  States,  but  has  not  been  taken  ad- 
vantage of  by  owners  of  timber  stumpage. 

210.  Public  Measures.  —  Within  the  last  decade  it  has  been 
demonstrated  that  the  fire   risk   can  be  largely  eliminated  in 
northern   and  western  states  by  the  enforcement  of   efficient 
fire  laws  and  the  organization  of  state  and  local  forces  of  fire 
wardens.     These  systems  are  as  yet  not  completely  successful, 
but  promise  to  become  so,  especially  in  states  where  politics 
has  been  eliminated  from  the  organization.     Education  of  the 
public,  punishment  of  offenders,  and  prompt  detection  and  sup- 
pression of  incipient  fires  form  the  groundwork  of  these  systems. 
Through  their  operation,   risks  will  eventually  be  reduced  to 
the  point   where   it   will  become  possible    to   insure   standing 
timber  from  fire. 

These  state  forces  are  aided  materially  by  semi-public  co-oper- 
ative associations  of  land  owners,  which  expend  large  sums  in 
fire  patrol  and  suppression.  The  operations  of  these  associa- 

*  "  Logging,"  by  Ralph  Clement  Bryant,  p.  37.  John  Wiley  &  Sons,  Inc.,  New 
York,  1913. 


214  FOREST  VALUATION 

tions  are  conspicuous  in  the  Pacific  Northwest,  and  have  ex- 
tended to  Michigan  and  New  England. 

The  importation  of  injurious  fungi  and  insects  is  now  guarded 
against  by  national  statutes  and  inspection.  One  serious  fungous 
disease,  the  white  pine  blister  rust,  has  been  checked  by  this 
means.  State  inspection  and  control  of  injurious  insects  and 
diseases,  supplemented  by  the  activities  of  the  national  govern- 
ment, furnish  a  means  of  preventing  future  outbreaks  similar  to 
that  of  the  chestnut  bark  disease.  Such  aid  should  be  chiefly 
preventive  in  character,  and  can  be  invoked  but  seldom  for  the 
control  of  native  insects. 

211.  Private  Measures.  —  Private  owners  may  be  forced  by 
state  legislation  to  take  measures  to  eliminate  unusual  fire  risks 
caused  by  their  own  operations.     Laws  making  brush  or  slash 
burning  compulsory,  especially  along  rights  of  way,  are  already 
adopted  in  some  states.     Top-lopping  is  intended  for  the  same 
purpose. 

In  addition  to  these  compulsory  private  measures,  owners  of 
forest  property  must  expect  to  take  extra  precautions  against 
fire,  similar  to  those  adopted  by  factories  and  stores  to  supple- 
ment the  work  of  the  fire  department.  Firebreaks  should  be 
constructed  and  maintained  for  the  protection  of  plantations, 
and  to  guard  against  excessive  hazards.  The  owner  and  his 
tenants  and  employees  should  be  prepared  for  fire  fighting  and 
equipped  with  the  most  suitable  tools  for  the  purpose. 

212.  Effect  of  Risks  on  the  Business  of  Forest  Production.  — 
Mature  timber,  while  in  danger  of  being  killed  by  fire,  insects 
or  disease,  or  blown  down,  can  usually  be  salvaged  with  only 
partial  loss.     To  the  greatest  danger  of  all,  fire,  it  is  moderately 
resistant.     Since  systematic  fire  protection  has  been  instituted  in 
the  North  and  West,  losses  have  averaged  less  than  two-tenths 
of  one  per  cent  annually,  on  the  value  protected.     The  risk  has 
never  deterred  investors  from  making  purchases  and  speculating 
on  values  of  stumpage. 

With  young,  immature  timber  and  reproduction,  the  same 
cannot  be  said.  A  comparison  of  risks  shows  that  the  hazard  is 
less  on  small  or  young  trees,  from  practically  all  sources  excepting 


RISKS  215 

fire.  But  the  risk  of  destruction  from  this  source  has  in  the 
past  been  so  great  as  to  constitute  a  prohibitive  hazard.  De- 
struction of  young  timber  is  a  total  loss,  for  there  is  no  salvage. 
The  dead  trees  are  quite  worthless,  and  even  constitute  an 
additional  expense  (§136).  The  period  over  which  the  invest- 
ment is  exposed  to  risk  is  correspondingly  longer  for  young 
timber  than  for  mature  trees,  which  can  be  removed  at  the 
owner's  convenience. 

As  long  as  the  public  and  the  land  owners  themselves  remained 
completely  indifferent  to  young  growth,  and  regarded  fires  on  cut- 
over  lands  as  of  no  consequence,  the  risk  incurred  in  the  business 
of  forest  production  was  prohibitive.  One  could  as  well  expect  to 
succeed  in  a  mercantile  business  when  thieves,  incendiaries  and 
dishonest  debtors  abounded,  and  there  existed  no  effective  law 
or  public  sentiment  to  check  their  operations.  The  first  step  in 
establishing  the  social  conditions  which  are  now  making  forest 
production  possible  was  the  creation  of  a  new  public  conscience 
and  understanding  on  the  subject  of  forest  property  and  forest 
fires.  The  elimination  of  theft  of  national  and  state  timber,  the 
tremendous  progress  in  fire  protection  in  northern  states,  and 
the  large  sums  spent  in  eastern  states  for  suppression  of  forest 
insects  and  diseases  indicate  that  this  constructive  work  is 
succeeding.  Under  proper  social  conditions,  such  as  have  been 
secured  in  France  and  Germany,  the  element  of  risk  in  forest 
production  becomes  less  than  that  incurred  in  almost  any  other 
form  of  enterprise.  The  employment  of  a  high  rate  of  interest 
in  forestry  is  merely  the  expression  of  this  undeveloped  state 
of  civilization  as  touching  forest  property,  and  should  not  be 
confused  with  the  returns  or  earning  power  of  forest  invest- 
ments. 


CHAPTER   XIV 
FIELD    APPRAISALS    OF   TIMBER    STUMPAGE 

213.  The  Scope  of  Field  Appraisals.  —  The  value  of  timber 
stumpage,  while  based  on  the  species,  quantity  and  quality  of 
the  timber,  is  determined  only  when  the  value  of  the  products 
f.o.b.  at  mill  and  the  intervening  costs  of  logging  and  milling 
have  been  appraised  (Chapter  XI) . 

The  field  appraisal  thus  deals  first,  with  the  reconnaissance 
of  the  timber  (§  no),  and  second,  with  the  appraisal  of  logging 
costs.  The  cost  of  milling,  depending  as  it  does  on  the  size  of 
the  mill  and  duration  of  the  operation  (§  173),  is  affected  by  the 
total  volume  of  timber  accessible  to  the  mill,  and  its  ownership, 
and  this  cannot  always  be  determined  when  examining  a  given 
tract.  Appraisals,  except  when  they  cover  a  large  area,  are 
therefore  most  definite  when  made  in  connection  with  mills 
already  operating. 

The  choice  of  general  means  of  transportation  must  occasion- 
ally be  left  to  the  field  examiner,  but  more  often  this  is  already 
indicated  by  local  custom,  and  it  remains  only  to  determine  on 
the  ground  whether  any  modifications  of  the  plan  are  necessary 
because  of  the  nature  of  the  topography  and  the  transportation 
problems  which  arise.  The  scope  of  the  actual  field  appraisal 
of  costs  is  usually  confined  to  ascertaining  the  local  costs  of 
logging.  These  costs  should  be  appraised  separately  for  each 
so-called  "logging  chance,"  or  separate  body  of  timber  forming 
a  logging  unit.  In  flat  regions,  the  division  of  a  larger  area 
into  units  is  not  important  and  depends  on  the  convenience  of 
locations  and  routes  for  main  spurs.  But  in  a  rough  or  moun- 
tainous country  the  "chance"  is  a  distinct  topographic  unit, 
such  as  a  gulch  or  small  basin,  containing  enough  timber  to 
furnish  employment  for  a  camp  of  reasonable  size  for  one  or 

216 


FIELD   APPRAISALS  OF  TIMBER   STUMPAGE  217 

more  seasons.  The  timber  on  such  a  unit  normally  comes  out 
over  the  same  route  —  a  branch  railroad  spur  or  road. 

Of  first  importance  in  the  examination  is  the  necessity  of 
sizing  up  this  local  transportation  problem,  deciding  upon  the 
best  method  of  removing  the  timber,  and  estimating  the  diffi- 
culties of  construction  and  cost  of  overcoming  them.  The  cost 
is  gauged,  not  on  the  basis  of  the  total  expense  of  construc- 
tion, but  with  relation  to  the  amount  of  timber  reached  (§  174). 
In  high  and  precipitous  mountains  it  is  necessary  to  decide 
how  far  up  the  slope  the  operator  can  go  without  exceeding 
the  permissible  cost  of  getting  out  his  logs. 

This  transportation  cost  is  thus  directly  dependent  upon 
the  estimate  of  the  standing  timber.  The  field  examination 
necessary  to  determine  it  is  either  a  part  of  the  work  of  timber 
reconnaissance,  or  some  additional  work  is  done  following  the 
completion  of  the  cruise,  to  make  sure  of  the  salient  points. 

214.  Timber  Reconnaissance :  The  Map.  —  In  the  timber 
examination  the  tract  is  ordinarily  crossed  and  recrossed  at 
intervals  of  40  rods  or  less,  and  the  intimate  and  systematic 
knowledge  of  the  topography  and  surface  thus  gained  permits 
the  formulation  of  the  plan  for  logging.  The  main  drainage 
and  its  tributaries  are  located  and  the  character  of  the  slopes 
and  surface  noted. 

This  knowledge,  when  necessary,  may  be  systematized  in 
the  form  of  a  topographic  map  which  shows  all  features  that 
affect  logging.  If  the  topography  is  so  level  that  transportation 
presents  no  difficulties,  such  a  map  serves  no  useful  purpose. 
If  the  map  does  not  indicate  conditions  with  sufficient  accuracy 
and  detail  to  enable  the  manager  to  plan  the  general  location 
of  his  transportation  system,  it  fails  of  its  purpose.  Actual 
lines  of  railroad  or  road  must  be  located  on  the  ground,  but  the 
entire  system  can  nearly  always  be  roughly  planned  from  a 
good  map.  Since  such  a  map  can  be  made  as  a  part  of  the  work 
of  timber  estimating,  the  expense  is  minimized  and  the  effort 
justified.  Otherwise  the  information  so  vitally  necessary  to 
the  planning  of  transportation  routes  exists  only  in  the  mind 
of  the  field  examiner  or  in  the  form  of  incomplete  notes. 


2l8  FOREST  VALUATION 

215.  Estimation  of  Standing  Timber.  —  The  estimation   of 
standing  timber  presents  one  of  the  most  difficult  problems  in 
the  business  of  lumbering.     This  might  not  be  true  were  there 
no  limits  to  the  cost  which  can  be  incurred  in  making  such  an 
estimate.     But  it  is  quite  possible  for  a  careful  detailed  measure- 
ment of  the  timber  on  a  tract  to  cost  over  $1.00  per  acre.     It  is 
a  recognized  precept  in  business  that  the  cost  of  stock  taking 
must  be  kept  as  low  as  possible,  for  the  work  adds  nothing  to 
the  value  or  the  profits  of  the  business,  and  is  necessary  merely 
as  a  basis  upon  which  to  plan  actual  operations. 

Methods  of  timber  estimating  are  determined  by  the  relation 
between  the  cost  of  doing  the  work  and  the  value  of  the  timber. 
The  amount  of  care  and  expense  justified  increases  with  rising 
stumpage  values.  Timber  is  always  estimated  in  terms  of  the 
product  which  has  the  highest  market  value,  or  is  most  readily 
saleable.  When  pulpwood  is  used,  the  cord  is  the  customary 
unit.  But  should  the  stand  be  situated  in  a  region  where  cord- 
wood  is  used  only  for  fuel,  the  number  of  ties  or  poles  and  the 
contents  in  lumber  of  suitable  trees  would  be  first  estimated 
and  only  the  residue  expressed  in  cords.  By  far  the  greater 
quantity  of  timber  is  estimated  in  terms  of  board  feet,  since 
it  is  used  in  this  form. 

216.  Log  Rules.  —  The  measurement  of  standing  trees  for 
board  foot  contents  is  beset  by  the  fundamental  difficulty  that 
no  commonly  accepted  standard  of  measurement  has  been  or  is 
likely  to  be  adopted  in  this  country  which  will  properly  express 
this  contents.     Innumerable  log  rules  are  in  use,  of  which  a 
few  are  now  widely  recognized.     But  these  rules  are  very  de- 
fective, seldom  giving  a  sufficiently  large  contents  for  logs  (§179). 
In  spite  of  this  fact,  it  will  seldom  be  possible  to  adopt  the  actual 
sawed  output  as  a  basis  for  timber  estimating,  as  long  as  logging 
contracts  and  other  woods  operations,  such  as  felling,  are  based 
on  the  old  standards  as  expressed  by  the  log  rules  in  common 
local  use.    Any  great  increase  in  the  measured  volumes  of  the 
logs  would  require  reduction  in  the  scale  of  payment  or  result 
in  loss  of  profits  by  the  millman.     The  only  safeguard  is  a 
knowledge  of  the  amount  of  overrun  usually  obtained  with  the 


FIELD   APPRAISALS  OF  TIMBER   STUMPAGE  219 

given  rule  in  the  class  of  timber  estimated  (§  179).  Quantities 
estimated  will  therefore  be  expressed  as  log  contents  measured 
by  the  local  rule,  but  in  computing  values  the  overrun  on  each 
thousand  feet  of  logs  will  be  allowed  for.  Log  rules  have  been 
devised  which  give  very  closely  the  actual  sawed  contents  of 
logs.  The  use  of  such  a  rule  insures  a  proper  standard  of  meas- 
urement for  the  contents  of  standing  trees.* 

217.  Closeness  of  Utilization  as  Affecting  Timber  Estimates. 
—  Another  factor  which  influences  timber  estimating  is  the 
closeness  with  which  the  timber  is  utilized  (§  186) .     Cheap  lumber 
necessitates  the  wasting  of  the  poorer  grades  of  boards,  as  the 
cost  of  manufacture  exceeds  the  sale  value.     Under  this  condi- 
tion, limby  tops,  defective  logs  and  small  trees  are  left  in  the 
woods.     In  such  forests  as  exist  in  Washington  State,  the  differ- 
ence between  utilizing  only  the  highest  grade  product  and  taking 
common  and  low  grade  lumber  may  make  50  per  cent  difference 
in  the  total  quantity  removed  (§  186).     In  general,  an  estimate  is 
made  on  the  basis  of  present  market  conditions,  and  does  not 
attempt  to  anticipate  future  values,  though  this  will  have  weight 
with  a  far-sighted  purchaser.     Estimates  made  in  past  periods 
were  low  compared  with  present  estimates  and  must  be  revised 
as  utilization  becomes  more  complete. 

218.  Field   Methods   of  Timber  Estimating.  —  With  these 
points  decided,  the  problem  remains  of  how  to  cover  the  area 
with  the  least  possible  cost.     It  is  desired  to  obtain  the  total 
quantity  of  timber,  by  species,  with  a  knowledge  of  sizes  and 
quality.     Cruisers   of   considerable   experience   hi   a   restricted 
locality  can  size  up  timber  by  walking  through  it,  and  from  their 
general  knowledge  of  what  similar  stands  have  cut  out,  will 
make  a  guess  at  the  total  stand.     This  method  is  comparatively 
useless  for  large  tracts,  or  with  men  of  lesser  experience  or  un- 
familiar with  a  region,  and  is  always  subject  to  large  errors. 

On  the  other  hand,  the  cruiser  may  go  to  the  trouble  of  meas- 
uring the  contents  of  each  tree  separately.  To  justify  this  course 
the  trees  must  be  very  valuable  and  the  area  small.  Woodsmen 

*  "  Forest  Mensuration,"  by  Henry  Solon  Graves,  Chap.  HI,  pp.  27-35.  John 
Wiley  &  Sons,  Inc.,  N.  Y.,  1906. 


220  FOREST  VALUATION 

almost  invariably  guess  at  the  contents  of  the  tree,  either  as 
a  whole  or  by  their  knowledge  of  the  contents  of  logs  of  cer- 
tain sizes.  A  better  method  is  to  use  tables  giving  volumes  in 
board  feet,  or  in  other  units,  for  average  trees  of  given  diameters 
and  heights,  when  such  tables  are  available  and  are  known  to  be 
reliable. 

219.  Strip  Methods.  —  By  far  the  greater  amount  of  timber 
estimating  is  done  by  methods  involving  the  measurement  of 
only  a  portion  of  the  stand,  in  an  effort  to  get  an  average  which 
will  apply  to  the  whole  area.     Even  if  all  the  trees  on  a  tract 
are  observed,  they  may  be  merely  counted,  and  an  average 
volume  obtained  by  guess  or  by  tallying  the  sizes  of  a  certain 
proportion  of  the  stand. 

The  most  widely  used  methods  consist  of  running  parallel 
compass  courses  through  the  area  at  definite  intervals,  and  meas- 
uring the  trees  standing  on  a  strip  of  a  definite  width  with  the 
course  as  a  center.  In  dense  brush,  or  with  small  timber,  this 
strip  may  be  but  4  rods  wide.  Where  tree  callipers  are  used 
to  get  the  diameter  of  each  tree  and  the  men  employed  to  do 
the  work  have  but  little  experience  in  timber  cruising,  this 
width  of  4  rods  is  seldom  exceeded.  More  experienced  woods- 
men, who  estimate  the  timber  by  eye,  usually  cover  a  strip 
8  or  10  rods  wide.  The  number  and  contents  of  the  trees  on 
these  strips  form  the  basis  of  the  estimate.  Should  the  strips 
so  measured  be  accepted  without  question  as  giving  an  average 
stand  for  the  whole  area,  the  total  estimate  is  found  by  using 
the  multiple  determined  by  the  per  cent  of  the  area  measured. 

220.  Errors  in  These  Methods.  —  But  this  is  seldom  the  case. 
Timber  is  never  uniformly  distributed  even  over  small  areas, 
but  varies  enormously  from  acre  to  acre  in  size  and  density. 
Topographic  and  site  factors  exercise  a  marked  influence  on 
the  stand.     The  timber  tends  to   run  in  belts  along  stream 
bottoms  and  slopes.     Chances  of  obtaining  a  better  average 
are  improved  by  arranging  the  strips  to  cross  these  belts,  which 
object  is  most  frequently  attained  by  running  up  and  down 
slopes  rather  than  along  them. 

For  a  given  per  cent  of  the  total  area  estimated,  the  chances 


FIELD   APPRAISALS   OF  TIMBER  STUMPAGE  221 

for  accuracy  are  improved  in  direct  ratio  to  the  size  of  the  area 
units  separately  measured.  Should  the  figures  be  desired  by 
separate  forty-acre  tracts,  an  estimate  covering  10  per  cent  of 
the  total  would  leave  opportunities  for  large  errors,  while  for 
a  section  of  640  acres,  10  per  cent  might  give  quite  close  results. 
Large  and  scattered  timber  requires  a  more  complete  estimate 
than  small  trees  densely  stocked.  Very  irregular  or  bunchy 
stands  may  require  greatly  increased  work  to  arrive  at  a  fair 
result.  One  method  of  dealing  with  this  fundamental  difficulty 
is  to  merely  accept  the  result  as  within  the  allowable  error  for 
such  work.  Astonishing  errors  creep  into  limber  estimates, 
even  with  experienced  men. 

221.  Types.  —  A  second  plan  is  to  subdivide  an  area  into  types 
by  means  of  a  sketch  map.     In  timber  estimating,  these  type 
divisions  are  for  the  purpose  of  improving  the  possibility  of 
getting  a  fair  average  stand.     They  are  really  stand  classes. 
Blank  or  open  areas  are  mapped  and  excluded  in  computing 
the  total  estimate.     Only  the  area  of  strips  run  within  a  given 
type  is  used  in  determining  the  stand  on  that  type.     The  amount 
of  work  which  this  method  entails  is  somewhat  greater  than  when 
the  timber  is  calculated  on  the  basis  of  the  whole  area,  but  this 
is  often  justified  and  the  plan  is  used  in  a  rough  form  by  nearly 
all  woodsmen. 

222.  Correction  Factor.  —  Another  method  of  improving  the 
final  estimate  without  measuring  every  tree  is  the  correction 
of  the  computed  total,  whenever  the  observations  and  judgment 
of  the  cruisers  indicate  its  necessity.    This  correction  must  be 
based  on  actual  inspection  of  the  entire  body  of  timber.    When 
running  strips,  short  side  trips  are  made  to  view  the  timber  which 
lies  outside  the  strip.     Should  this  timber  run  heavier  or  lighter 
than  that  measured,  the  total  will  be  reduced  or  increased  by  an 
estimated  per  cent.     This  plan  must  not  be  confused  with  the 
method  of  guessing  at  the  total  stand,  for  it  is  based  on  a  careful 
estimate,  tree  by  tree,  of  a  portion  of  the  area.     Should  it  be 
impossible  for  any  reason  to  actually  inspect  the  remaining 
timber,  there  can  be  no  basis  for  correcting  the  result,  which 
must  stand  for  what  it  is  worth. 


222  FOREST  VALUATION 

223.  Quality  of  Timber.  —  To  judge  of  the  quality  of  the 
timber,  attempts  have  been  made  to  grade  logs,  according  to 
the  relative  value  of  their  contents,  into  perhaps  four  classes. 
This  is  actually  done  in  Puget  Sound  where  a  well-established 
log  market  exists  and  logs  are  purchased  on  the  basis  of  the  log 
grade  or  class.     The  difficulty  with  such  a  basis  ordinarily  is 
that  logs  vary  in  value  from  several  sources;  knots  or  sap  in 
young  timber,  rot  and  wind  shake  in  old  trees.     A  dividing 
line  or  standard  is  not  sufficiently  definite,  nor,  except  under 
the  conditions  cited  above,  are  logs  ever  sold  on  this  basis. 
They  are  paid  for  at  a  flat  rate,  according  to  the  average  value 
of  the  contents.    The  only  recourse  of  the  cruiser  is  to  attempt 
to  size  up  the  quality  of  the  trees  by  their  size,  apparent  age, 
clearness  or  freedom  from  knots,  and  soundness  or  freedom  from 
interior  defects.     With  a  knowledge  of  the  average  per  cent 
of  grades  produced  in  mills  cutting  similar  timber,  the  cruiser 
estimates  the  per  cent  of  each  grade  that  the  stand  will  cut. 
Should  the  timber  be  older,  larger  or  better  than  the  average 
stands,  he  increases  his  estimate  of  the  higher  grades  to  corre- 
spond. 

224.  Reports.  —  The  information  which  should  be  given  in 
a  satisfactory  report  on  a  tract  of  timber  is  shown  under  the 
following  heads. 


I.     Area. 


1.  Description  or  location  of  specific  tract. 

2.  Area. 

3.  Subdivisions  of  area. 

a.  Blanks. 

Water. 
Barren. 
Burns. 

b.  Reproduction  or  immature  timber. 

c.  Forest  types. 

d.  Age  classes,  where  distinguishable. 


FIELD   APPRAISALS  OF  TIMBER   STUMPAGE  223 

II.     Volume. 

1.  Species:    Separate    estimates    for   conifers    and 

hardwoods,  and  for  each  commercial  species. 

2.  Volume  in  merchantable  units. 

a.  Board  feet. 

b.  Cords. 

c.  Pieces  (poles,  ties,  etc.). 

3.  Deductions  from  gross  volume. 

a.  Dead  timber  (probable  durability). 

b.  Cull,  due  to  defects  (rot,  wind  shake). 

III.  Damage. 

1.  Rot:   Extent,  character  and  amount  of  damage. 

2.  Fire:   Standing   dead   timber,   damage   to    live 

timber. 

3.  Insects:     Location,    prevalence,    character    of 

damage. 

4.  Windfall:  Location,  amount  and  condition. 

IV.  Quality. 

1.  Size  (if  necessary,  for  two  or  more  size  classes). 

a.  Average  diameters,  at  4^  feet  (or  at  stump 

height). 

b.  Average  heights. 

Number  of  merchantable  i6-ft.  logs. 
Total  height  of  tree  in  feet. 

2.  Form  of  bole. 

a.  Straight  or  crooked. 

b.  Taper,  expressed  in  inches  per  i6-ft.  log. 

c.  Clear  length.    Limbs,  character  of  knots. 

3.  Grades. 

Per  cent  of  probable  output  in  each  of  several 
standard  grades  for  species  and  locality. 

V.     Young  timber. 

1.  Species. 

2.  Area,  in  acres  or  in  per  cent  of  total  area. 


224  FOREST  VALUATION 

3.  Average  age.     Range  of  ages. 

4.  Sizes.      Average   and   range  of   diameters   and 

heights. 

5.  Condition.     Thrift,  damage,  with  causes. 

6.  Chances    of    survival.     Competition  with  older 

timber,  and  with  worthless  species,  or  brush. 

7.  Probable  commercial  value  at  maturity. 

VI.     Soil .   Quality.     Agricultural  value. 

VII.     Logging   conditions;    summary  for    "logging    chance" 
rather  than  for  each  subdivision  of  estimate. 

1.  Topography.     By  map  or  description. 
Character  of  slopes.     Obstacles  to  logging. 

2.  Surface. 

a.  Underbrush. 

b.  Rock. 

c.  Character  of  bottom. 

3.  Transportation. 

a.  Streams,  character  for  driving,  cost  of  im- 

provements. 

b.  Routes  for  roads,  or  railroad  spurs. 

c.  Methods  of  skidding  and  hauling. 

VIII.     Modifications  of  logging  required  by  silvicultural  demands. 
Summary  for  logging  chance. 

1.  Amount  and  character  of  merchantable  timber 

to  be  left  standing. 

2.  Methods  of  brush  disposal,  and  precautions  re- 

quired for  protection  of  young  timber  (if  not 
summed  up  for  larger  areas  as  a  whole). 

IX.     General  conditions  affecting  appraisal. 

1.  Market  value  of  lumber,  or  price  basis. 

2.  Size  of  mill,  and  cost  of  milling,  with  profits. 

Investment  required. 

3.  Cost  of  main  transportation  system. 


FIELD   APPRAISALS   OF  TIMBER   STUMPAGE  225 

X.     Specific  conditions  affecting  appraisal. 

1.  Specific  costs  of  logging  the  "chance." 

2.  Specific  appraisal  of  value  of  standing  timber 

per  unit  of  log  scale,  based  on  total  cost 
and  total  quantity,  or  distributed  according 
to  value  of  species  (§  180). 

XI.  Appraised  value  of  standing  timber,  by  species,  for 
specific  units  of  product,  modified  for  overrun  to 
apply  to  standing  timber. 


CHAPTER  XV 

COMPARISON   OF  FOREST  VALUES   WITH   AGRI- 
CULTURAL VALUES 

225.  Agricultural  Soils.  —  Agricultural  soils  are  soils  which 
will  produce  agricultural  crops  continuously  in  paying  quan- 
tities, under  proper  cultivation  and  treatment.     Many  classes 
of  soils  will  produce  scant  crops  for  short  periods,  after  which 
they  must  be  abandoned.     Such  soils  should  seldom  be  used 
for  crops  at  all  but  kept  under  forest  cover.     Permanent  agri- 
cultural fitness  of  soil  is  determined  by  six  factors:    quality  of 
the  soil  itself,  topography  or  slope,  climate,  water  supply,  the 
personal  or  human  factor,  and  the  economic  factors. 

226.  Quality  of  Soil.  —  Soils  to  be  agricultural  must  be  free 
from  excessive  quantities  of  rock,  and  not  too  sandy,   since 
loose-textured  soils  will  not  retain  sufficient  moisture  or  soluble 
plant  food  to  permit  satisfactory  growth.      They  should  be 
underlaid  by  a  permeable  subsoil  which  permits  sufficient  drain- 
age.    Deep  sands,  and  stiff  clay  underlaid  by  hard-pan,   are 
familiar  types  of  non-agricultural  lands. 

227.  Slope.  —  The  slope  is  important,  since  crops  must  be 
cultivated,  and  upon  steep  slopes,  if  not  terraced,  the  loosened 
surface  washes  away,  deep  gullies  are  formed  and  the  land  is 
permanently  ruined  for  agriculture.     Slopes  varying  from  10  to 
20  per  cent,  according  to  rainfall  and  quality  of  soil,  will  prevent 
permanent  cultivation. 

228.  Climate.  —  Crops  will  grow  in  all  but  the  coldest  climates 
if  given  sufficient  water.     But  in  mountainous  regions,  lands 
at  high  elevations  resemble  regions  near  the  arctic  circle.     Frosts 
occur  every  month  in  the  year,  and  the  growing  of  all  agricul- 
tural crops,  except  a  poor  quality  of  hay,  is  prevented.     Such 
lands  are  non-agricultural,  regardless  of  the  quality  of  soil. 

226 


COMPARISON  OF  FOREST  WITH  AGRICULTURAL  VALUES      227 

229.  Water.  —  In    regions    of    sufficient    rainfall,    low-lying 
lands  are  often  swampy.     Drainage  transforms  such  soils  into 
permanent  agricultural  lands  of  high  value.     In  dry  regions, 
irrigation  brings  otherwise  desert  soils  under  cultivation.     Trees 
ordinarily  require  fully  as  much  soil  moisture  as  crops.     Desert 
lands  are  therefore  of  no  value  for  forestry,  but  undrained 
swamp  land  will  produce  valuable  though  slow-growing  species. 

230.  Personal  Factors.  —  The  personal   element  is  a  large 
factor   in   successful   agriculture.     Experience  is  the  foremost 
need,  but  industry,  economy  and  good  business  capacity  are 
equally  helpful.     The  advancement  of  agricultural  knowledge 
by  experiment  stations,  and  the  general  trying  out  of  new 
methods,  often  make  success  possible  on  soils  and  in  climates 
which  were  once  thought  too  hostile  to  permit  of  agricultural  use. 

231.  Economic  Factors.  —  The  development  of  transporta- 
tion, and  increasing  values  for  farm  products,  have  a  stimulating 
effect  on  agriculture,  and  farms  can  be  made  to  pay  in  regions 
near  large  markets,  which  would  be  too  poor  to  cultivate  in  less 
accessible  localities.    This  last  factor,  coupled  with  the  advance 
in  knowledge  of  farming  methods,  tends  to  bring  more  and  more 
land  into  agricultural  use,  and  the  standard  of  classification 
between  agriculture  and  forestry,  for  this  reason,  can  never  be 
a  hard  and  fast  one. 

But  the  differences  between  good  and  poor  soil  will  remain 
as  great  as  ever  and  some  soil  will  always  be  too  poor  to  farm. 
In  densely  populated  eastern  states  sandy  and  rocky  land  in 
abundance  is  found,  upon  which  the  inhabitants  eke  out  a  mis- 
erable existence  and  which  no  amount  of  skillful  management 
will  make  into  profitable  farms. 

232.  Comparison  of  Agriculture  with  Forestry  as  a  Source  of 
Livelihood.  —  The  use  of  land  for  the  production  of  agricultural 
crops  differs  in  many  important  particulars  from  its  use  for  the 
production  of  timber  crops.     Agriculture,  the  direct  source  of  all 
food  supplies,  yields  immediate  livelihood  to  the  farmer,  whose 
returns  are  based  on  an  annual  cycle.    A  large  element  of  labor 
enters  into  crop  production,  both  for  preparing  and  clearing  the 
soil,  and  hi  actual  cultivation  and  harvesting.    Added  to  this  is 


228  FOREST  VALUATION 

the  investment  in  buildings,  fences,  machinery  and  live  stock. 
Agriculture  requires  large  continuous  outlays  per  acre,  and  in 
return  must  produce  adequate  income  to  compensate  the  farmer. 
If  the  soil  is  unsuited  to  agriculture,  this  outlay,  which  is  as 
necessary  on  poor  soil  as  on  good,  is  inadequately  rewarded, 
and  the  farmer  impoverished. 

Trees  grow  best  on  good  agricultural  soils  and  produce  their 
greatest  values  in  such  situations.  But  timber  crops  do  not 
provide  as  stable  a  source  of  livelihood  as  agriculture.  The 
revenue  from  sales  of  timber  is  realized  only  after  the  lapse  of 
the  long  period  of  growth.  Mature  stands  may  be  sold  or  held 
at  will  and  the  income  varied  largely  at  the  discretion  of  the 
owner  as  long  as  there  are  trees  of  suitable  size  for  cutting. 

Over  long  periods,  even  at  best,  the  net  annual  revenue  from 
forest  property  is  much  lower  than  from  agricultural  crops. 
Relatively,  forestry  may  be  far  the  more  profitable  business. 
The  expenses  per  acre  are  correspondingly  lower  than  in  agri- 
culture. While  not  giving  a  solid  basis  for  continuous  liveli- 
hood except  in  the  business  of  lumbering,  which  requires  large 
areas  of  land,  forestry  on  the  other  hand  does  not  require  con- 
stant time  and  attention.  Timber  if  given  protection  from  fire 
will  grow  without  cultivation.  It  therefore  forms  an  ideal  in- 
vestment for  surplus  income,  but  a  poor  basis  for  an  individual 
living. 

The  economic  advantage  of  forestry  over  agriculture  becomes 
evident  only  on  poor  agricultural  soils.  Trees  of  fair  quality 
will  still  grow  on  soils  utterly  unfit  for  farming,  and  owing  to  the 
small  expense  attandent  on  this  crop,  will  yield  profitable  returns 
on  such  soils. 

233.  Non-agricultural  Soils.  —  Since  food  and  livelihood  and 
permanent  homes  are  more  important  to  mankind  than  fuel 
and  timber,  soils  which  will  repay  the  farmer  should  be  devoted 
to  farm  crops.  But  the  attempt  to  cultivate  soils  essentially 
non-agricultural  leads  to  very  serious  results  both  for  the  indi- 
vidual and  for  society.  Soils  are  non-agricultural  when  they 
cannot  continue  year  after  year,  with  proper  care,  to  produce 
paying  crops.  Non-agricultural  soils,  when  cultivated,  either 


COMPARISON   OF   FOREST   WITH   AGRICULTURAL  VALUES      2  29 

wash  away  by  erosion,  blow  into  sand  dunes,  lose  their  small 
store  of  fertility  by  too  active  drainage,  or  for  other  reasons  fail 
to  respond  to  the  efforts  of  the  farmer. 

234.  Exploitation  of  Land  Purchasers.  —  Intelligent  farmers 
refuse  to  buy  or  work  such  lands.     Uninformed  purchasers, 
either  foreigners  or  city   emigrants  unused  to  farming,    buy 
these  lands  because  they  are  cheap.     They  are  even  less  able  to 
make  a  living  upon  them  than  are  the  more  experienced  farmers 
who  have  passed  them  by.    The  effort  results  in  financial  and 
often  in  moral  bankruptcy.    Lands  of  this  character  thus  change 
hands  often,  and  since  the  real  estate  business  is  based  on  land 
transfers,  it  thrives  on  such  conditions. 

Whatever  hurts  the  individual  hurts  the  whole  community. 
The  exploitation  of  well-meaning  land-hungry  investors  by 
professional  land  locators  and  real  estate  sharks  is  a  business 
closely  akin  to  more  pronounced  forms  of  swindling.  Local 
sentiment  in  such  communities  will  be  largely  molded  by  these 
selfish  predatory  interests  and  will  resist  attempts  to  properly 
classify  such  land  as  non-agricultural.  Thus  a  condition  is 
created  containing  limitless  possibilities  of  evil  to  the  public  at 
large. 

235.  Land  Classification.  —  The  solution  of  this  problem  lies 
in  the  scientific  classification  of  lands,  to  determine  whether  or 
not  agriculture  is  possible.     If  unsuitable  for  farms,  then  the 
lands  fall  naturally  into  the  class  of  forest  soils,  and  should  be 
removed  from  the  market  as  agricultural  land,  and  devoted  to 
forest  production.     The  best  way  to  accomplish  this  removal  is 
for  the  states  to  purchase  such  soils  for  forest  reserves  or  for  the 
national  government  to  acquire  them  for  stream  protection. 

236.  Basis  of  Comparison  of  Agricultural  and  Forest  Values  of 
Land.  —  To  compare  the  value  of  land  for  agriculture  with  its 
value  for  forestry,  each  value  must  if  possible  be  expressed  in 
money.     In  each  case  the  basis  of  value  is  future  net  income 
capitalized  (§62).     If  we  include  for  botrTuses  all  items  of  future 
income,  minus  future  costs,  and  can  appraise  this  income  and  its 
present  value  accurately,  the4  comparison  will  reveal  the  relative 
value  of  the  property  and  determine  whether  the  soil  is  best  suited 


230  FOREST  VALUATION 

to  farming  or  forestry.  Unfortunately,  the  uncertainties  affect- 
ing the  determination  of  these  future  items,  in  both  cases,  prevent 
a  satisfactory  mathematical  comparison  of  such  values.  Yet 
whatever  the  basis  on  which  the  comparison  is  made,  it  is 
founded  on  the  economic  relations  which  such  calculations  set 
forth. 

237.  Expectation  Value  of  Agricultural  Land.  —  The  basis 
of  agricultural  value  is  the  net  revenue  from  crops.     The  actual 
cost  of  labor  and  use  of  machinery  is  deducted  from  the  sale 
value  of  the  crops  and  the  average  net  return  is  capitalized. 
Owing  to  the  fact  that  on  small  farms  the  proprietor  puts  in 
his  own  labor  and  raises  food  for  his  family,  this  net  income  is 
not  often  accurately  computed.     Cash  rent  paid  for  farm  land 
separates  the  costs  from  the  income,  since  the  tenant  presumably 
gets  only  his  just  share,  including  profit,  and  the  rent  represents 
the  net  income  earned  by  the  soil.     Since  this  is  annual,  it  is 

capitalized  by  the  formula (XII),  on  the  basis  that   the 

o.op 

farm  will  produce  this  rental  without  deteriorating.  A  farm 
earning  $5  per  acre  rent  will,  at  5  per  cent,  be  worth  $100  per 
acre. 

238.  Sale    Value    of    Agricultural    Land.  —  Improved   farm 
land  is  transferred  with  sufficient  frequency  to  establish  sale 
values,  in  any  region  where  farming  is  a  well-developed  industry. 
These  sale  values  will,  on  the  whole,  coincide  quite  closely  with 
the  capital  or  appraised  values  of  farms  based  on  net  income. 
But  traditions,  demand,  and  increasing  or  declining  population 
affect  farm  values  and  prices  to  a  great  extent.     Values  of  farm 
property  are  sluggish  at  times  and  again,  in  boom  periods,  out- 
strip conservative  appraisals  of  income.     In  this  the  human 
element  in  price  making  is  seen  to  play  a  large  part   (§§17, 

59,  69.) 

239.  Timber  as  an  "  Agricultural  "  Value.  —  Improved  farm 
land  is  not  the   true  basis  of   comparison  with   forest   land. 
Land  in  its  wild  state  ranges  from  heavily  timbered  tracts 
through  all  degrees  of  stocking  and  of  young  timber,  to  natural 
prairies  needing  only  to  be  broken  for  a  crop.     Land  which 


COMPARISON   OF   FOREST  WITH  AGRICULTURAL  VALUES      231 

has  been  stripped  of  timber,  but  is  covered  with  stumps  which 
interfere  with  the  cultivation  of  the  surface  and  prevent  the  use 
of  machinery,  is  the  condition  in  which  the  prospective  farmer 
in  most  cases  has  to  accept  property  in  timber  regions  to-day. 
In  former  times,  timber  itself  had  no  value,  hence  the  cost 
of  removing  it,  including  the  burning  of  the  logs,  gave  such 
lands  a  low  initial  value.  It  is  still  necessary  to  cut  and  remove 
standing  timber  from  agricultural  soils,  but  the  timber  now  has 
a  stumpage  value  and  its  removal  will  cost  the  owner  nothing, 
while  its  sale  supplies  him  with  capital  with  which  he  can  un- 
dertake the  work  of  clearing  the  land  of  stumps.  The  presence 
of  merchantable  timber  upon  such  soils  thus  aids,  apparently, 
in  establishing  agricultural  use. 

In  heavily  timbered  regions,  this  seldom  works  out.  Stump- 
age  cannot  be  marketed  at  will  and  in  many  regions  must  await 
the  slow  development  of  transportation  and  the  gradual  cutting  of 
the  more  accessible  timber.  The  owner  cannot  afford  to  sacrifice 
it  for  agriculture,  except  on  a  small  portion  of  the  area  and, 
consequently,  sells  this  land  with  its  timber  to  some  lumber 
company.  In  time,  the  land  is  stripped  of  timber  and  the 
stump  land  is  offered  to  purchasers  for  agricultural  use. 

Timber  values  on  agricultural  soils  cannot  be  regarded  in  any 
sense  as  agricultural  values,  but  are  the  equivalent  of  so  much 
money  capital  to  the  owner  of  the  land.  Granting  that  pur- 
chasers who  secure  timber  obtain  more  valuable  property  than 
those  who  get  only  stump  land,  it  is  still  evident  that  the  agri- 
cultural value  of  forest  land  must  be  based  solely  on  the  land 
bare  of  all  timber. 

240.  Stump  Land  versus  Cleared  Land.  —  The  value  of 
stump  land  is  less  than  that  of  open  meadow  or  prairie  land 
in  its  wild  state,  by  the  amount  of  the  extra  cost  of  clearing  and 
preparing  it  for  cultivation.  The  crops  are  the  only  source  of 
value,  and  since  improved  land  is  now  bearing  crops  its  value 
rests  on  a  firm  basis.  Between  this  value  and  that  of  stump  land 
is  interposed  the  future  costs  of  clearing  and  breaking,  and  the 
time  necessary  to  do  the  work.  Fencing,  development  of  water, 
and  buildings  must  be  added,  before  agriculture  can  be  sue- 


232  FOREST  VALUATION 

cessful.  These  future  costs  depress  the  real  value  of  stump 
land,  and  cause  a  wide  divergence  between  the  true  values  of 
wild  land  and  improved  farms. 

241.  Cost  of  Clearing  Stump  Lands.  —  The  appraisal  of  the 
cost  of  clearing  land  is  not  difficult,  but  if  based  on  the  actual 
cost  of  wages  for  the  labor  required  in  clearing  up  ground  at 
one  operation,  it  is  apt  to  be  too  high.     Land  is  seldom  cleared 
in  that  way,   except  by  land  companies  supplied  with  large 
capital.    The  settler  clears  gradually,  using  his  own  labor  at 
slack    seasons,   cultivating   between   the    stumps,    grazing    the 
land,  and  allowing  the  stumps  to  rot.     The  roots  of  hardwood 
and  sap  pine  stumps  decay  in  from  three  to  ten  years  and  the 
stumps  are  easily  gotten  out.     The  stumps  of  heart  pine  and 
certain  other  conifers  do  not  rot  readily  but  will  pull  much  more 
easily  after  a  few  years  than  at  first.     The  loss  in  time  is  great, 
since  the  full  utility  of  the  soil  for  crops  is  not  attained  for  years. 
The  settler  may  even  be  investing  an  amount  of  labor  and  capital 
in  the  clearing  for  which,  judged  commercially,  he  will  never 
be  repaid.     But  clearing  will  be  attempted  successfully  even  on 
lands  on  which  its  cost  apparently  exceeds  the  final  value  of 
the  land.     Therefore  the  cost  of  clearing,  provided  the  soil  is 
good,  should  not  be  regarded  as  indicating  a  negative  expectation 
value  for  stump  land.     Should  the  cost  exceed  the  value  of 
cleared  land,  a  very  low  value  for  stump  land  is  indicated,  but 
this  value  will  still  be  positive  in  most  cases. 

242.  Sale  Value  of  Stump  Lands.  —  Sale  values  for  stump 
lands  are  often  falsely  or  inaccurately  determined  and  are  set 
at  far  too  high  a  figure.     This  is  due  to  the  lack  of  general 
knowledge  of  the  costs  and  delays  of  clearing.     The  values  for 
highly  productive  improved  lands,  perhaps  bearing  orchards, 
are  compared  with  stump  lands,  to  the  enhancement  of  value 
for   the   latter  in    the   minds  of   purchasers,   many   of   whom 
know  nothing  of  the  problems  involved.     It  is  safe  to  say  that 
without  the  necessary  additional  capital  to  hire  the  clearing 
done,  such  lands  can  never  be  developed  by  this  class  of  inves- 
tors out  of  the  income  from  the  property,  while  persons  of 
small  means  cannot  buy  stump  land  at  high  initial  prices  and  ever 


COMPARISON  OF  FOREST  WITH  AGRICULTURAL  VALUES      233 

expect  to  lift  the  mortgages  which  they  must  usually  accept. 
In  contrast  to  boom  sale  values  upon  such  lands,  the  appraised 
value  of  stump  land  should  be  reasonably  low  compared  with 
improved  tracts  in  the  same  neighborhood. 

243.  Summary  of  Elements  of  Value  for  Forest  Land.  —  The 
elements  of  value  which  must  be  considered  in  arriving  at  the 
value  of  forest  lands  are: 

Value  of  mature  or  merchantable  timber. 
Expectation  value  of  young  timber. 
Value  of  land  based  on  future  timber  crops. 
To  these  values  must  be  added: 

Value  of  improvements  as  roads,  fire  lines. 
Value  of  protective  influence  of  the  forest. 

The  determination  of  value  for  merchantable  timber  is  dis- 
cussed in  Chapter  X.  Actual  prices  received  for  similar  timber 
are  commonly  accepted  as  indicating  this  value. 

The  value  of  young  timber  and  of  land  is  found  by  the  methods 
described  in  Chapter  VI,  when  an  appraisal  is  necessary. 

Roads  and  other  improvements  do  not  influence  value  on 
the  basis  of  what  they  cost,  but  by  their  effect  in  cheapening 
transportation,  lowering  fire  risks  and  increasing  the  net  income 
or  lowering  the  rate  of  interest  (§§211  and  68).  In  proof  of  this 
statement  it  is  recognized  that  in  agricultural  appraisals  the  cost 
of  dwellings  and  other  improvements  on  farms  is  not  the  basis 
on  which  the  farm  is  valued,  although  they  add  to  its  value  by 
providing  the  immediate  facilities  for  deriving  the  income  by 
cultivation. 

The  value  of  the  protective  influence  has  been  discussed  in 
Chapter  VII  (§  146).  This  value  benefits  adjoining  property 
rather  than  the  land  itself,  but  is  an  important  factor  when 
weighing  the  relative  merits  of  agricultural  versus  forest  use. 
Fortunately,  slopes  valuable  for  their  protective  forest  cover 
are  usually  too  steep  to  be  tilled  without  inducing  erosion,  and 
the  demonstration  of  this  fact  would  at  once  prevent  the 
classification  of  such  soils  as  agricultural  by  an  intelligent 
investigator. 


234  FOREST  VALUATION 

Of  these  five  items  of  value  only  the  revenue  from  sale  of 
mature  timber  is  immediately  available.  This  is  comparable 
with  the  revenue  from  the  current  crop  on  agricultural  land. 
When  ready  to  harvest,  it  greatly  exceeds  the  latter  as  it  rep- 
resents a  long  accumulation. 

244.  Value  of  Young  Timber  as  a  Part  of  the  Value  of  Forest 
Soil.  —  When  comparing  the  value  of  land  for  forestry  with 
agricultural  values,  we  assume  that  the  land  has  some  value 
for  agriculture.  Absolute  forest  soils,  whose  agricultural  use  is 
impossible,  need  not  be  valued  in  order  to  determine  the  class 
to  which  they  belong. 

Where  agriculture  is  possible,  but  its  profitableness  is  ques- 
tionable, and  the  cost  of  clearing  is  high,  the  value  of  the  land 
for  forestry  may  greatly  exceed  any  value  for  farming.  Here 
a  calculation  of  forest  values  will  be  of  great  assistance  in  deter- 
mining the  best  disposition  of  the  land. 

Agricultural  soil  is  always  regarded  as  bare  land  and  the  value 
as  that  of  the  soil  itself,  not  including  crops  which  may  be  grow- 
ing. This  is  merely  because  of  the  short  crop  period.  In 
reality  the  standing  crop  increases  the  value  of  the  property 
while  present  and  is  the  source  of  this  value,  and  a  purchaser  of 
the  land  must  either  permit  the  former  owner  to  harvest  the 
crop  or  pay  him  for  it.  Forest  land  to  be  compared  with  agri- 
cultural land  on  the  same  basis  must  be  bare  of  timber.  But 
it  is  the  timber  crop  that  gives  the  land  whatever  forest  value 
it  has  (§  1 1 6).  In  actual  practice,  forest  land  is  seldom  in  this 
bare  condition.  As  seen  in  Chapter  VII,  the  actual  value  of 
forest  property  depends  upon  the  closeness  of  the  date  of  realiz- 
ing the  income  from  the  timber.  The  value  of  the  timber  may 
be  separated  from  land  if  necessary,  but  this  separation  is  arti- 
ficial (§135).  The  real  value  of  forest  property  is  based  on  the 
actual  condition  of  the  stand,  its  age  and  size.  Forest  values 
differ  from  agricultural  values  in  that  they  fluctuate  over  long 
periods  with  the  growth  and  removal  of  the  crops  instead  of 
maintaining  a  reasonably  constant  relation  from  year  to  year. 
The  lowest  ebb  is  represented  by  bare  land,  and  in  a  system  of 
clear  cutting  this  condition  is  attained  but  once  in  the  period  of 


COMPARISON  OF   FOREST  WITH  AGRICULTURAL  VALUES      235 

growth  of  the  crop,  just  previous  to  planting.  In  any  system 
of  natural  seeding,  and  especially  with  selection  cutting,  the  value 
of  forest  "land"  never  reaches  this  low  point,  but  is  maintained 
at  a  higher  level  by  the  presence  of  partly  grown  timber  which 
will  bring  in  revenue  in  a  shorter  period  than  a  full  crop 
rotation. 

If  young  timber  is  present  on  forest  soils,  it  is  not  possible 
to  consider  this  timber  as  having  no  value  without  rejecting  the 
basis  of  all  values,  which  is  future  income.  We  cannot  consider 
merely  the  forest  value  of  the  land  itself,  for  this  is  derived 
wholly  from  timber.  The  expectation  value  of  the  young 
timber  is  more  definite  than  the  same  value  calculated  for  the 
soil  itself  (§  1 1 6),  as  it  is  nearer  and  more  certain  than  that  from 
non-existent  future  crops,  or  "soil."  If  land  bearing  young 
timber  is  cleared  for  agriculture,  the  forest  value  sacrificed  is 
greater  than  that  of  forest  land  by  just  the  difference  that  the 
age  of  this  timber  makes  in  the  present  value  of  the  income 
expected  from  it.  To  ignore  this  value  would  be  the  same  as  to 
consider  a  half  grown  crop  of  wheat  as  adding  nothing  to  the 
sale  value  of  agricultural  land. 

Nor  can  we  ignore  the  future  income  from  young  timber  as 
an  element  of  forest  value  on  the  grounds  that  this  is  not  a 
present  but  a  future  value,  perhaps  not  attainable  for  several 
decades.  If  agricultural  values  were  based  merely  on  the  revenue 
from  the  next  year  or  decade,  the  capital  value  of  farm  land 
would  be  much  lower  than  it  is.  All  future  revenue  is  included 
in  such  agricultural  values  as  surely  as  it  must  be  included  in 
finding  the  present  value  of  forest  property  (§85).  The  mere 
fact  that  forest  income  is  irregular  makes  it  no  less  necessary  to 
value  the  entire  future  income  in  finding  the  value  of  the  prop- 
erty for  forestry. 

245.  Sale  Value  of  Forest  Property.  —  As  in  the  case  of 
agricultural  soils,  sales  are  the  generally  recognized  basis  of 
value  for  forest  property,  soil  and  standing  crops  included. 
But  the  sale  value  of  forest  property  may  suffer  from  ignorance 
or  lack  of  recognition  of  the  true  worth  of  the  property  (§  in). 
If  young  timber  has  been  allowed  to  burn  up  in  the  past,  or  if 


236  FOREST  VALUATION 

insufficient  time  has  elapsed  since  logging  began  on  the  virgin 
forest,  the  fact  that  young  timber  will  grow  into  a  valuable 
merchantable  stand,  or  second  growth,  is  not  generally  appreci- 
ated. The  forester,  a  specialist  on  appraisal  of  growing  timber, 
can  estimate  this  value  on  its  true  basis.  But  the  public  will 
place  a  much  lower  estimate  on  the  property,  or  may  ignore 
altogether  the  element  represented  by  the  young  timber  and 
value  the  land  itself  on  an  arbitrary  basis  not  related  to  its 
use  for  forest  production,  but  based  on  grazing  or  other  uses. 

Purchasers  of  land  follow  a  sound  policy  in  acquiring  it  at  as 
low  a  value  as  possible,  and  if  bought  for  forestry  they  gain 
by  this  condition  of  undeveloped  sale  values.  But  as  a  basis  for 
classification,  the  acceptance  of  existing  sale  values  of  land  and 
young  timber,  merely  because  the  public  are  not  familiar  with 
true  values,  is  wholly  inexcusable.  When  this  condition  is 
further  aggravated  by  accepting  an  inflated  agricultural  value 
for  unimproved  stump  lands,  the  comparison  is  unfavorable  to 
the  securing  of  a  true  and  lasting  classification. 

246.  Discrimination   against   Forest   Values.  —  Where   eco- 
nomic pressure  is  strong  for  the  listing  and  opening  of  lands  for 
new  settlers,  the  tendency  is  to  deliberately  ignore  the  expec- 
tation value  of  young  timber  as  well  as  of  the  land,  and  to  con- 
sider only  the  mature  timber  as  indicating  the  sum  of  forest 
values.     Or,  perhaps,  the  forest  value  of  the  land  is  recognized, 
but  not  that  of  young  trees.     This  is  even  more  inconsistent 
than  the  first  plan.     The  argument  is  advanced  that  the  value 
of  young  timber  will  not  be  realized  for  many  years  while  that 
of  agricultural  crops  applies  to  the  present  moment.    But  if 
these  timber  values  are  based  on  present  stumpage  prices  (§  195) 
and  properly  discounted  to  the  present,  it  must  be  evident  from 
the  discussion  in  Chapter  VI  that  expectation  value  is  a  true 
present  value,   strictly  comparable  with    that   for   agriculture 
(§  244).     Rejection  of  such  appraisal  can  be  justified  only  in  two 
ways,  —  when  forest  values  are  actually  less  than  agricultural 
values  for  stump  land,  or  on  the  basis  of  political  expediency. 

247.  Discrimination  in  Favor  of  Forest  Values.  —  The  rec- 
ognition of  increasing  future  prices  brings  an  element  of  specu- 


COMPARISON  OF   FOREST  WITH  AGRICULTURAL  VALUES      237 

lation  into  such  appraisals,  and  when  this  is  done,  the  present 
values  thus  found  are  no  longer  based  on  present  but  on  future 
conditions.  It  is  this  element,  and  not  the  discounting  of  future 
income  to  the  present,  which  would  unfairly  alter  the  basis  of 
appraisal  in  favor  of  forest  values.  A  parallel  case  would  be 
found  were  it  estimated  that  prices  for  farm  crops  would  in- 
crease and  that  the  value  of  land  at  present  should  be  based  on 
an  appraisal  of  this  future  increase  in  annual  income. 

Future  growth  in  volume  is  a  justifiable  assumption,  as  is 
also  an  improvement  in  quality  of  timber  and  of  unit  price  based 
on  this  quality,  to  conform  to  the  higher  prices  now  received  for 
similar  grades  (§§  183,  184).  But  the  discounting  of  future  in- 
creases in  the  general  price  level  for  timber  is  as  little  justified 
in  the  case  of  valuation  for  comparison  with  agriculture  as  it  is 
in  valuing  damages  to  young  timber.  In  either  case,  present 
values  must  be  based  on  present  prices,  and  future  increases  may 
be  used  only  by  the  owner  in  computing  possible  or  speculative 
profits. 

248.  Results,  when  Values  of  Bare  Land  are  Compared.  — 
From  the  above  discussion  it  is  assumed  that  a  true  comparison 
of  forest  with  agricultural  values  is  based  on  a  computation  or 
appraisal  of  the  expectation  or  present  capital  value  of  the 
property  for  each  use,  the  forest  values  present  in  the  form  of 
timber  and  land  being  compared  with  the  value  of  stump  land 
for  agriculture.     The  highest  value  for  both  purposes  will  always 
be  found  on  the  richest  agricultural  soils.     But  it  will  seldom 
if  ever  be  true  that  the  forest  value  of  bare  soil  will  exceed  its 
agricultural  value  if  the  soil  is  fairly  adapted  to  crop  production. 
Only  upon  the  poorer  or  non-agricultural  soils  will  land  itself, 
even  at  a  low  forest  value,  be  worth  more  for  wood  crops  than 
for  agriculture. 

249.  Results,   when    Full    Value    of    Property   is    used    in 
Comparison.  —  With   the  growth  of  the   timber,  however,  a 
corresponding  increase  takes  place  in  the  forest  values  of  the 
property  or  "land,"  until  at  some  point  during  this  growth  the 
actual  present  value  of  the  timber  and  land  exceeds  the  agri- 
cultural values.    At  any  time  previous  to  this,  it  is  justifiable 


238  FOREST  VALUATION 

to  destroy  the  young  timber  and  clear  the  land,  although  in  doing 
so  a  greater  value  is  sacrificed  or  wasted  than  if  stump  land  only 
were  so  used.  The  destruction  of  merchantable  timber  in 
former  days  was  justified  on  this  basis,  since  the  value  of  the 
land  for  agriculture  exceeded  the  total  timber  values  present. 

But  pioneer  conditions  have  passed,  and  the  destruction  of 
merchantable  timber  values  is  no  longer  thought  of  except 
where  these  pioneer  conditions  are  reproduced  by  lack  of  trans- 
portation and  markets.  Even  as  the  former  settlers  found 
that  with  increasing  values  the  uncleared  portions  of  the  farm 
became  a  source  of  unexpected  wealth,  so  in  the  future  it  will 
pay  the  settler  to  protect  young  growth  and  keep  a  portion  of 
his  farm  in  timber. 

The  mature  timber  upon  agricultural  land  adds  a  forest  value 
to  the  value  of  the  stump  land.  The  land  is  worth  just  as 
much  more  to  the  settler  as  the  price  he  can  get  for  his  standing 
timber.  The  only  drawback  is  that  until  this  is  sold  and  re- 
moved he  cannot  begin  his  clearing.  But  upon  most  claims  there 
is  enough  poorly  timbered  soil  to  occupy  the  time  and  energies 
of  the  settlers  until  such  sale  is  effected.  Should  there  be  no 
such  openings,  and  the  entire  claim  be  heavily  timbered,  agri- 
cultural use  is  inevitably  postponed  until  logging  commences, 
for  the  relative  value  of  the  timber  is  so  great  as  to  preclude 
any  other  course. 

250.  National  Forest  Policy  in  Land  Classification.  —  In 
classifying  national  forest  land  in  pursuance  of  the  policy  of 
granting  homesteads,  land  should  not  be  listed  for  settlement 
while  the  total  forest  values  exceed  the  agricultural  value  of 
stump  land.  This  necessitates  the  sale  and  removal  of  mature 
timber  from  agricultural  soils,  previous  to  listing.  But  owing 
to  the  pressure  for  land  throughout  the  west  the  tendency  is 
at  present  to  ignore  the  appraised  value  of  immature  timber 
and  even  the  capital  value  of  forest  land,  and  to  permit  the 
listing  of  lands  containing  a  certain  amount  of  merchantable 
timber.  This  reservation  is  beneficial  to  the  settler  for  it  gives 
him  a  subsidy  or  value  in  addition  to  his  land. 

Since  this  procedure  clearly  sacrifices  all  forest  values  except 


COMPARISON   OF  FOREST  WITH  AGRICULTURAL  VALUES      239 

the  present  saleable  timber,  it  will  inevitably  result  in  listing 
rapidly  all  lands  of  agricultural  value  whether  or  not  they  are 
covered  with  young  trees,  provided  only  that  the  merchantable 
stand  is  not  too  dense  or  valuable.  If  this  policy  is  demanded 
by  dearth  of  farm  land  in  these  regions  it  should  be  carried  out, 
but  the  basis  upon  which  the  classification  is  made  must  be 
frankly  recognized  as  expediency  rather  than  sound  appraisals 
of  value. 

251.  Reciprocal  Values  in  Forestry  and  Agriculture.  —  Forest 
and  agricultural  values  cannot  be  considered  as  wholly  sepa- 
rate. On  every  agricultural  unit  there  is  need  of  a  certain 
amount  of  forest  land  to  furnish  wood  for  fuel,  fence  posts  and 
even  lumber,  and  as  shelter  for  stock  and  windbreaks.  In 
treeless  prairies  the  planted  grove  greatly  enhances  the  desira- 
bility of  the  whole  property  as  a  residence  and  adds  in  this  way 
far  more  to  the  sale  value  of  the  farm  than  is  accounted  for 
by  the  possible  revenue  which  this  grove  could  produce.  In 
wooded  regions  the  labor  of  clearing  is  so  great  that  two  or  even 
three  decades  must  elapse  before  the  entire  farm  will  be  brought 
under  cultivation  by  the  efforts  of  the  farmer,  unless  aided  by 
investing  the  necessary  capital  in  clearing  on  a  large  scale. 
Meanwhile  the  woodlots  will  grow  at  an  appreciable  rate  and 
young  timber  at  first  but  a  few  feet  tall  will  become  large 
enough  for  use.  In  many  regions  this  wooded  portion  may  also 
be  grazed  without  undue  injury  to  the  trees,  if  the  latter  have 
sufficient  height. 

Every  effort  should  be  made  by  owners  of  such  tracts  to  spare 
and  encourage  areas  of  reproduction  and  of  young  timber,  more 
especially  when  such  growth  occurs  on  the  poorer  portions, 
steeper  slopes  and  more  inaccessible  parts  of  the  farm.  In 
this  way  each  part  of  the  farm  unit  is  put  to  its  best  use,  the 
maximum  returns  are  obtained,  and  the  sale  value  of  the  entire 
property  will  usually  exceed  the  sum  of  the  forest  and  agricul- 
tural values  when  separately  considered. 


APPENDIX 

Formulae. 

Summary  of  Formulas  of  Compound  Interest. 

Definitions  of  Symbols. 

Summary  of  Formulae  of  Forest  Valuations. 
Compound  Interest  Tables  (Table  VI). 
Tables  of  Logarithms  (Table  VII). 


SUMMARY  OF  FORMULA  OF  COMPOUND  INTEREST 


Character  of  payments. 

Values  at  the  end,  future 
values,  cost. 

Values  at  the  beginning,  present 
values,  capitalized  income,  capi- 
tal value,  expectation  value. 

Single  sums  

V0Xi.opn                         (I) 

^                   on 

Temporary  rentals, 
annual  

intermittent  .... 

r(i.op--i) 

r(i.o/>»-i) 

(IV) 
(VI) 
(VIII) 

o.op 
r'(i.op"«-i) 

o.op(i.opn) 
r'(i.opnt-i) 

i.opn-i 

(i.opn  —  i)  i.opnt 

i.opn  —  i 

(i.opn  —  i)  i.opnt 

Perpetual  rentals, 
intermittent  

annual  

00 
00 

r' 

(IX) 
(X) 

i.opn—  i 

i.opn  —  i 

Conversion  of  intermittent  into  annual  rentals,  • —     _ —  X  o.op        (XIII) 


(XIV) 


Ratio  of  income  to  capital  investment,  x  =  100  (  y  ^ — 


240 


APPENDIX  241 

SUPPLEMENTARY  FORMULA 

r—  (i.op*  -  i)  |  i.opb  +  ^  (i.op»-  i).         (Ilia) 
R(i.opn-  i).  (Illb) 

(Xa) 


+  ^0^-? 

DEFINITIONS  OF  SYMBOLS 

a  —  Year,  previous  to  w,  for  which  value  or  cost  of  property 
is  sought. 

d  —  Im°f ,  ratio  used  in  Formulae  P3  and  P4  in  deter- 

o.op 

mining  the  amount  (Z)  to  be  written  off  annually 
for  profit  and  depreciation. 

e  —  Annual  expenses,  constituting  one  year's  net  outlay. 

g  —  First  term  of  a  geometric  series. 

m  —  Interval  between  intermittent  yields  in  a  many-aged 
forest. 

n  —  Period  required  to  produce  a  crop  of  timber.  Rotation. 
Interval  between  yields  produced  by  even-aged  stands 
of  timber. 

p  —  Standard  rate  of  interest  in  forestry. 

q  —  Ratio,  or  multiple,  for  a  geometric  series. 
q%  —  Per  cent  of  legitimate  profit  to  be  allowed  in  logging 
and  milling,  or  in  logging  alone,  in  stumpage  ap- 
praisals. 

r  —  Annual  rental,  regarded  either  as  income  or  outlay. 

r'  —  Intermittent  rental,  due  at  regular  intervals  greater 

than  one  year. 

r%  —  Per  cent  of  legitimate  profit  to  be  allowed  in  milling 
alone,  in  stumpage  appraisals. 

5  —  Per  cent  of  overrun  per  thousand  board  feet,  log  scale. 

/  —  Number  of  payments  expected  in  a  temporary  inter- 
mittent rental. 


242  APPENDIX 

x  —  Rate  of  dividends  or  interest  earned  by  an  investment. 

z  —  Per  cent  of  value  to  be  written  off  annually  for  depre- 
ciation in  Formula  PZ- 

A  —  Original  capital  investment  in  assets  subject  to  depre- 
ciation. 

C  —  Cost  of  initial  silvicultural  and  protective  measures, 

incurred  in  first  year. 

Cd}  Ce,  Cj  —  Cost   of   silvicultural   and   protective  measures, 
incurred  in  subsequent  years,  d,  e  and  /. 

D  —  Total  amount  to  be  written  off  for  depreciation  during 
the  life  of  an  enterprise. 

E  —  Expectation  or  capital  value  of  annual  expenses,  e, 

by  Formula  XII,  — • 
o.op 

aFc  —  Total  cost  of  forest  property,  including  both  land  and 
growing  stock  or  timber,  for  the  year  a.     For  year  n, 
substitute  HFC  or  Fc. 
F8  —  Sale  value  of  forest  property,  both  land  and  timber,  in 

the  year  n  or  when  timber  is  mature. 
aFs  —  Expectation  value  of  this  sale  value  for  the  year  a, 

previous  to  the  year  n  or  year  of  sale. 

Fv  —  Expectation  value  (capital  value)  of  forest  property, 
including  both  land  and  timber.  Applicable  to  both 
even-aged  and  many-aged  stands. 

*FV  —  Expectation  value  of  forest  property  for  year  a  pre- 
vious to  year  n. 

Gc  —  Cost  of  growing  stock  or  standing  timber. 
aGv  —  Expectation  value  of  growing  stock,  or  standing  timber, 
separate  from  land,  for  the  year  a  previous  to  year  n. 
L  —  Total  amount  of  loss  or  damages  to  forest  property. 
LC  —  Logging  costs. 

LD  —  Depreciation  of  logging  investments. 
MC  —  Milling  costs. 
MD  —  Depreciation  of  milling  investments. 

P  —  Profit  or  enterpriser's  gain,  remaining   after  paying 

interest  at  p  per  cent  on  capital  investment. 
Q  —  Sum  of  terms  in  a  geometric  series. 


APPENDIX  243 

R  —  Expectation  or  capital  value  of  the  sum  of  payments 

constituting  a  rental. 
5  —  Sale  value  of  lumber  or  of  logs.     Value  of  soil. 

Sc  —  Cost  of  soil  and  of  permanent  improvements. 

5S  —  Sale  value  of  soil. 

Sv  —  Expectation  or  capital  value  of  forest  soil. 
Tp,  Tq,  Tr  —  Net  income  from  sale  of  thinnings  in  years  />, 
q  and  r. 

V  —  Value  of  a  single  sum. 

FQ  —  Value  of  sum  at  beginning  of  period. 

Va  —  Future  value  in  year  a  of  the  sum  of  items  of  income 
and  expense  on  a  crop  of  timber. 

Vn  —  Value  of  a  single  sum  at  end  of  a  period  of  w  years. 

Vr  —  Future  value  of  the  sum  of  payments  constituting  a 
rental. 

W  —  Final,  wrecking  or  residual  value  of  assets  in  logging 
or  milling,  after  writing  off  total  depreciation. 

X  —  Annual  sum  required  to  be  written  off  for  depreciation. 

Y  —  Sale  value,  or  appraised  value,  of  timber  stumpage. 

Yf  —  Sale  value,  or  appraised  value,  of  timber  stumpage, 
resulting  from  fire  or  other  damage. 

Ym  —  Stumpage  value  of  1000  board  feet  of  manufactured 
lumber,  used  as  basis  to  determine  Y. 

Z  —  Annual  sum  which  combines  income  or  profit  on  in- 
vested capital  with  depreciation,  the  sum  constitut- 
ing one  of  a  series  of  equal  annual  payments. 

SUMMARY  OF  FORMULAE  IN  FOREST  VALUATION 

COSTS 

Cost  of  a  single  even-aged  stand  of  timber. 

INDEX     ART. 
LETTER 

Gc=(C  +  5c  +  £)i.o/>n-(5c  +  £)     ....    A       105 
Gc  =  (C  +  Sc  +  E)i.o/>"+Cd(i.o/O+Ce(i.o^-') 
+  C/i  .o/>»-')  -  Tp  (i  .o^-")  -  r,(i  .o#-«) 

-Tr(i.opn~r}  -  (Sc+E) A!      105 

Cost  of  a  forest,  including  timber  and  soil,  for  year  a. 

°FC  =  (C  +  SC  +  E)i,opa  -  E A2       105 


244 


APPENDIX 


Cost  of  a  normal  many-aged  forest. 

Gc  = -— 

o.op 


INDEX     ART. 
LETTER 


.    .    As      109 


VALUES 

Sale  value  of  a  single  even-aged  stand  in  year  n,  in- 
cluding value  of  soil. 

F,=  Y  +  Sa. B        112 

Expectation  or  capital  value  of  above  for  year  a,  pre- 
vious to  year  n. 

aFs  =  -  ^"    'J^      ~  E Bl       II2 

7+  Ss+  E  +  Tp(i.opn-p)  +  rfl(i.of-«) 

aFs  = *\  -  P — I %   B2      II2 

i. op"-1 

Expectation  or  capital  value  of  forest  property  in 
the  year  n,  previous  to  removal  of  crop. 

V  —  C 

Tf        v  _t_      (r*   i    i?\  r* 

rv=x-\ (C-h-Cr) C        114 

I  .opn  —  i 

+r,(i.of )-c-d(i.o^-4) 

-Ce(i.opn-e}-Cf(i.opn-') 

,„  ^i       114 

i.opn  —  i 

Expectation  or  capital  value  of  forest  property  in 
the  year  a,  previous  to  year  n. 

(Y-0^_E D 

i.opn  -  i 

Tp          Tq    +Tr(i.opn)      c 

i.opp      i.opq          i.opr 

*  i.opa 

_^_    "7^~~    i.of  ,_ 

I.O^"  -   I 

y  +  ^  +  £-£ D2      II6 

T..0pn~a 


APPENDIX  245 


INDEX     ART. 
LETTER 


Expectation  or  capital  value  of  forest  soil. 


Sv=     Y~C    -(C  +  E)  ........    E       116 

i.  op    —  i 

)  +  Tr  (i.0jp~) 


i.opn  -  i 

Ei      116 
Soil  rent  =  Sv  X  o.op £2      116 

Expectation  or  capital  value  of  a  many-aged  forest 
in  year  m,  just  subsequent  to  removal  of  crop. 


Expectation  or  capital  value  of  a  many-aged  forest 
in  year  a,  previous  to  year  m. 


Expectation  or  capital  value  of  a  many-aged  forest 
producing  annual  income. 


o.op 

Expectation  or  capital  value  of  a  many-aged  forest 
for  irregular  yields  and  periods. 


i.opn  —  i 

F3      118 


Expectation  or  capital  value  of  growing  stock  or 
timber  separate  from  soil,  in  year  a,  previous  to 
year  n,  for  a  single  even-aged  stand. 


119 


246  APPENDIX 

INDEX     ART. 
LETTER 
Expectation  or  capital  value  of  growing   stock  or 

timber  separate  from  soil,  in  year  a,  previous  to 
year  m,  for  a  many-aged  stand. 

an          ^  ~T"  PV  ~t~  Ei         f  0  ,-,•>  „, 

v  =  "To/r17"  ~  '  *        ^  .......       *      II9 

PROFITS 

Profits  in  destructive  lumbering,  on  timber  and  land, 
for  year  n  or  at  time  of  sale  of  timber. 

P  =  Y  +  S8  +  E-  (C  +  Sc  +  E)i.o/>»    .     .     .     H       122 
P  =  Y  +  S,  +  E  +  TP  (i.o#-*)  +  Ts  (i.op-<) 

+  rr  (i.o/>"-o  -  (c  +  sc  +  E)  i.0/>» 

-  Cd  (i  .o/O  -  Ce  (i  .o/>w-)  -  Q  (i  .o/>»--0  .     H!       122 
Profits  in  destructive  lumbering,  on  timber  alone,  for 
year  n. 

P=Y  +  Sc  +  E-(C  +  Se  +  E)i.op\    .     .     .     K       123 
Profits  in  destructive  lumbering,  on  timber  alone,  for 
year  a,  previous  to  year  n. 

P  =  Y  +  Sc  +  E  -  (C  +  Sc  +  £)  i  .of.  .     .     .     K!       124 

i.  op" 


p 


i.opn~c  i.opp-°       i.opg~a       i.opr~a 

Profits  in  continuous  forest  production,  for  year  n. 

P  =  Y  +  Sv  +  E  —  (C  +  Sc  +  E}  i.opn.  .     .     .    L        125 
Profits  in  continuous  forest  production,  for  year  a, 
previous  to  year  n. 

Y  4-  s  -f  E 
P  =  —  — ^ (C  +  Sc  +  E)  T..opa   ...     LI       126 

p  =  «pB  -  aFc L2       126 

P  =  (Sc  -  Sv)  i.opa L4       126 

Profits  in  continuous  forest  production  for  year  o, 
previous  to  origin  of  crop. 

P  =  Sv  -  Sc L3      127 


APPENDIX 


247 


INDEX    ART. 
LETTER 

INTEREST  EARNED 
Rate  of  interest  earned  on  soil  capital. 

Y  +  SV  +  E-(C  +  E)  i  .opn 
T..oxn  =  -  z  -  -*  -  '-  -  Z-  .....    N       120 

Oc 

Rate  of  jnterest  earned  on  soil  and  initial  investments. 
Y  +  S9  +  E-E(i.op*) 

Sc  +  c       "  .......  Nl    I29 

Rate  of  interest  earned  on  entire  investment. 


Mean  annual  forest  per  cent. 

x  =  f  X  p  .............     N3      129 

•Jc 

Current  annual  forest  per  cent. 

TB+1  -Yn-e 
—- 


\ 

jioo      .......    N4      129 


Fn1  -Yn-e 


Current  annual  forest  per  cent,  for  normal  forest. 


DAMAGES 
Damages  to  mature  timber. 

L  =  Y  -  F'.    .     ...........    O       140 

Damages  to  young  timber  for  year  a,  previous  to 
year  w. 

F-  Y' 


i.opn~a' 
Damages  to  timber  and  soil,  for  year  a. 


Oi       141 


L==  Y  +  Sv  +  E      c  +  E,  _  (c  +  £)>  ^     ^     ^     Q2 
- 


248  APPENDIX 

INDEX     ART. 
LETTER 

DEPRECIATION 
Depreciation,  Method  A. 

X  -*%&-.     ...  P        17S 

I.0pn  -  I 

Depreciation,  Method  B. 

y      D      A-W 

X  =  —=—       —  ...........     P!       i7c 

w  w 

Depreciation,  Method  C. 


..........      P2         175 

Depreciation,  Method  D. 


Z  =  A  (o.o/O  +  —  (Hunter's  formula).      .     .     .    P4       175 

GEOMETRIC  SERIES 
Sum  of  rentals,  increasing  temporary  series. 

e-*^  ............  Q'     8o 

Sum  of  rentals,  decreasing  temporary  series. 


Sum  of  rentals,  increasing  perpetual  series. 

Q  =  oo  ...............     Q3         80 

Sum  of  rentals,  decreasing  perpetual  series. 

e  =      .............  Qi    8o 


APPENDIX  249 

INDEX     ART. 
LETTER 

STUMPAGE  VALUES 

Stumpage  appraisal  on  basis  of  manufactured  lumber; 
profits,  a  per  cent  of  operating  costs. 

Ym=S-(LC+MC  +  D)-q%(LC  +  MC+D}     R        177 
Ym  =  S  -{MC+MD+LC+LD}  -r%(MC+MD) 

-q%(LC  +  LD)  .........     R!       177 


Stumpage  appraisal  on  basis  of  manufactured  lumber; 
profits,  a  per  cent  of  sale  value. 

Ym  =  ^^       -(LC  +  MC  +  D)     .....     R2      177 

Stumpage  appraisal  on  basis  of  manufactured  lumber; 
profits,  a  per  cent  of  margin  between  operating  costs 
and  sale  value. 


......        a      177 

Stumpage  appraisal  on  basis  of  manufactured  lumber; 
reduction  to  log  scale. 

F=  F.(i.os)  ............     R4      179 

TABLE  VI 
COMPOUND  INTEREST  TABLES 

The  period,  n  years,  in  left-hand  column. 

Column  I,  Formula  I.  —  Future  value  of  $i  at  end  of  n  years. 

Column  II,  Formula  II.  —  Present,  expectation  or  capital  value  of  $i  due  in  n 

years. 
Column  III,  Formula  III.  —  Future  value  at  end  of  n  years  of  an  annual  rental 

of  $i  payable  n  times. 
Column  IV,  Formula  IV.  —  Present,  expectation  or  capital  value  of  an  annual 

rental  of  $i  payable  n  times. 


250 


APPENDIX 


PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0050 

•  9950 

I.  0000 

•  9950 

.0100 

.9901 

2.0050 

1.9851 

.0151 

.9851 

3-0150 

2.9702 

.0202 

.9802 

4-0301 

3.9505 

•0253 

•  9754 

5.0503 

4.9259 

.0304 

•  9705 

6.0755 

5.8964 

•0355 

•  9657 

7-1059 

6.8621 

.0407 

.9609 

8.1414 

7.8230 

•  0450 

.9561 

9.  1821 

8.7791 

10 

.0511 

•  9513 

10.2280 

9.7304 

11 

.0564 

.9466 

11.2792 

10.6770 

12 

.0617 

.9419 

12.3356 

11.6189 

13 

.0670 

•  9372 

13-3972 

12.5562 

14 

.0723 

.9326 

14.4642 

13.4887 

15 

-0777 

.9279 

15.5365 

14.4166 

16 

.0831 

•  9233 

16.6142 

15-3399 

17 

.0885 

.9187 

17.6973 

16.2586 

18 

•  0939 

.9141 

18.7858 

17.1728 

19 

.0994 

.9096 

19.8797 

18.0824 

20 

.1049 

•  9051 

20.9791 

18.9874 

21 

.  1104 

.9006 

22.0840 

19.8880 

22 

.1160 

.8961 

23.1944 

20.7841 

23 

.1216 

•    .8916 

24.3104 

21.6756 

24 

.1272 

.8872 

25.4320 

22.5629 

25 

-1328 

.8828 

26.5591 

23.4456 

26 

-1385 

.8784 

27.6919 

24.3240 

27 

.1442 

.8740 

28.8304 

25.1980 

28 

.1499 

.8697 

29-9745 

26.0677 

29 

•  1556 

•  8653 

31.1244 

26.9330 

30 

.1614 

.8610 

32.2800 

27.7941 

31 

.1672 

.8567 

33.4414 

28  .  6508 

32 

.1730 

•  8525 

34.6086 

29-5033 

33 

.1789 

.8482 

35.7817 

30-3515 

34 

.1848 

.8440 

36.9606 

31-1955 

35 

.1907 

.8398 

38.1454 

32-0354 

36 

.1967 

•  8356 

39.3361 

32.8710 

37 

.2027 

.8315 

40.5328 

33.7025 

38 

.2087 

.8274 

41-7354 

34.5299 

39 

.2147 

.8232 

42.9441 

35-3531 

40 

.2208 

.8191 

44.1588 

36.1722 

41 

.2269 

.8151 

45-3796 

36.9873 

42 

.2330 

.8110 

46.6065 

37.7983 

43 

.2392 

.8070 

47-8306 

38.6053 

44 

•  2454 

.8030 

49.0788 

39-4082 

45 

.2516 

•  7990 

50.3242 

40.2072 

46 

•2579 

•  7950 

5I-5758 

41.0022 

47 

.2642 

.7910 

52-8337 

4I-7932 

48 

.2705 

.7871 

54.0978 

42  -  5803 

49 

.2768 

•7832 

55.3683 

43.3635 

50 

.2832 

•7793 

56.6452 

44.1428 

55 

•  3IS6 

.7601 

63.1200 

47.9782 

60 

.3488 

.7414 

69.7600 

51.7020 

65 

.3829 

•  7231 

76.5800 

55-2764 

70 

.4178 

•  7053 

83.5600 

58.9364 

75 

•  4536 

.6879 

90.7200 

62.4745 

80 

•  4903 

.6710 

98.0600 

65.7988 

85 

.5280 

•  6545 

105  .  6000 

69.1099 

90 

-5665 

•  6383 

113.3000 

72.3268 

95 

.6061 

.6226 

121.2200 

75-4747 

100 

.6467 

.6073 

129.3400 

78-5449 

105 

.6882 

•  5923 

137.6400 

81.5306 

100 

•  7309 

•  5777 

146.1800 

84-4531 

115 

.7746 

.5635 

154.9200 

87-2985 

120 

.8194 

•  5496 

163.8800 

90.0736 

APPENDIX 


251 


i  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0100 

.9901 

I.  0000 

.9901 

.0201 

•9803 

2  .OIOO 

1.9704 

.0303 

.9706 

3  •  0301 

2.9410 

.0406 

.9610 

4.0604 

3-9020 

.0510 

•9515 

5-  1010 

4-8534 

-06lS 

.9420 

6.1520 

5-7955 

.O72I 

.9327 

7-2135 

6.7282 

.0829 

•9235 

8.2857 

7-6517 

•0937 

•9143 

9.3685 

8.5660 

10 

.  1046 

•9053 

10.4622 

9.4713 

11 

•US? 

.8963 

11.5668 

10.3676 

12 

.1268 

.8874 

12.6825 

"•2551 

13 

.1381 

.8787 

13-8093 

12.1337 

14 

•1495 

.8700 

14.9474 

13-0037 

15 

.l6lO 

•  8613 

16.0969 

13-8651 

16 

.  1726 

•  8528 

17.2579 

14.7179 

17 

.1843 

.8444 

18.4304 

15-5622 

18 

.I96l 

.8360 

19.6147 

16.3983 

19 

.2081 

•8277 

20.8109 

17  .2260 

20 

.22O2 

.8195 

22.0190 

18.0456 

21 

.2324 

.8114 

23.2392 

18.8570 

28 

.2447 

.8034 

24.4716 

19-6604 

23 

.2572 

•  7954 

25-7163 

20.4558 

24 

.2697 

.7876 

26.9735 

21.2434 

25 

.2824 

.7798 

28.2432 

22.0232 

26 

•2953 

.7720 

29.5256 

22.7952 

27 

.3082 

.7644 

30.8209 

23  -  5596 

28 

•3213 

•  7568 

32.1291 

24.3164 

29 

•3345 

•  7493 

33.4504 

25-0658 

30 

•3478 

.7419 

34.7849 

25.8077 

31 

•  3613 

•  7346 

36.1327 

26.5423 

32 

•3749 

•  7273 

37-4941 

27.2696 

33 

.3887 

.7201 

38.8690 

27.9897 

34 

.4026 

•  7130 

40.2577 

28.7027 

35 

.4166 

•  7°59 

41.6603 

29  .  4086 

36 

.4308 

.6989 

43.0769 

30.1075 

37 

•4451 

.6920 

44.5076 

30.7995 

38 

•4595 

.6852 

45-9527 

31-4847 

39 

.4741 

.6784 

47-4123 

32.1630 

40 

.4889 

.6717 

48.8864 

32.8347 

41 

.5038 

.6650 

50.3752 

33.4997 

42 

.5188 

.6584 

51.8790 

34.i58i 

43 

•5340 

.6519 

53-3978 

34.8100 

44 

•5493 

•6454 

54-93i8 

35-4554 

45 

.5648 

.6391 

56.4811 

36-0945 

46 

•5805 

.6327 

58-0459 

36.7272 

47 

•5963 

.6265 

59-6263 

37-3537 

48 

.6122 

.6203 

61  .2226 

37-9740 

49 

•  6283 

.6141 

62.8348 

38.5881 

50 

.6446 

.6080 

64.4632 

39.1961 

55 

.7284 

.5786 

72.8400 

42.1430 

60 

.8166 

.5505 

81.6600 

44.9521 

65 

•  9093 

•  5238 

90  .  9300 

47-6247 

70 

.0066 

.4983 

100.6600 

50-1644 

75 

.1090 

.4742 

110.9000 

52.5841 

80 

.2166 

.4500 

121.6600 

54-8858 

85 

.3296 

•  4292 

132.9600 

57.0742 

90 

.4485 

.4084 

144  .  8500 

59.1750 

95 

•  5733 

.3886 

157-3300 

61  .  1394 

100 

.7046 

•  3697 

170.4600 

63.0259 

105 

.8425 

•  3518 

184.2500 

64.8197 

110 

.9875 

•  3347 

198.7500 

66.5272 

115 

3  •  1399 

.3185 

213.9900 

68.1518 

120 

3.3001 

.3030 

230.0100 

69.6979 

252 


APPENDIX 


if  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0150 

.9852 

i  .0000 

-9852 

.0302 

.9707 

2.0150 

1-9559 

•0457 

•  9563 

3-0452 

2.9122 

.0614 

.9422 

4.0909 

3.8544 

-0773 

.9283 

5-1523 

4.7826 

•0934 

.9145 

6.2290 

.1098 

.9010 

7-3230 

6.5082 

.1265 

.8877 

8.4328 

7-4859 

•1434 

.8746 

9-5593 

8.3605 

10 

•  1605 

.8617 

10.9027 

9.2222 

11 

.1779 

.8489 

11.8633 

10.0711 

12 

.1959 

.8364 

13-0412 

10.9075 

13 

.2130 

.8240 

14-2368 

II-73I5 

14 

-2318 

.8118 

15.4504 

12-5434 

15 

.2502 

•  7999 

16.6821 

13-3432 

16 

.2690 

.7880 

17-9324 

14-1313 

17 

.2880 

.7764 

19.  2014 

14.9076 

18 

.3073 

.7649 

20.4894 

15.6726 

19 

•3270 

.7536 

21.7967 

16.4262 

20 

•3469 

.7425 

23-1237 

17.1686 

21 

•3671 

.7315 

24-4705 

17.9001 

22 

-3876 

.7207 

25-8376 

18.6208 

23 

.4084 

.7100 

27.2251 

19-3309 

24 

•429S 

.6995 

28.6335 

20  .  0304 

25 

•4509 

.6892 

30.0630 

20.7196 

26 

•4727 

.6790 

31.5140 

21.3986 

27 

.4948 

.6690 

32.9867 

22.0676 

28 

.5172 

.6591 

34-48I5 

22.7267 

29 

.5400 

.6494 

35.9987 

23-3761 

30 

•5631 

.6398 

37-5387 

24.0158 

31 

•S86S 

.6303 

39.1018 

24.6461 

32 

.6103 

.6210 

40.6883 

25.2671 

33 

•6345 

.6118 

42  .  2986 

25-8790 

34 

.6590 

.6028 

43-9331 

26.4817 

35 

-6839 

•  5939 

45-5921 

27-0756 

36 

.7091 

•  5851 

47.2760 

27  .  6607 

37 

.7348 

•5764 

48-9851 

28.2371 

38 

.7608 

.5679 

50.7199 

28.8051 

39 

.7872 

•  5595 

52.4807 

29.3646 

40 

.8140 

•5513 

54-2679 

29.9158 

41 

.8412 

•5431 

56.0819 

30.4590 

42 

.8688 

•  5351 

57.9231 

30.9940 

43 

.8969 

•  5272 

59.7920 

31-5212 

44 

-9253 

•5194 

61.6889 

32.0406 

45 

•9542 

•  5117 

63.6142 

32.5523 

46 

•  983S 

.5042 

65.5684 

33-0565 

47 

•  0133 

.4967 

67.5519 

33-5532 

48 

•0435 

.4894 

69.5652 

34.0426 

49 

.0741 

.4821 

71.6087 

34-5247 

50 

.1052 

•  4750 

73-6828 

34-9997 

55 

.2679 

.4409 

84.5296 

37-27I5 

60 

•4432 

•  4093 

96.2147 

39-3803 

65 

.6320 

•  3799 

108.8000 

41-3373 

70 

•83SS 

•  3527 

122.3640 

43-1549 

75 

.0546 

•  3274 

136.9670 

44.8409 

80 

.2907 

.3039 

152.7110 

46.4073 

85 

•5450 

.2821 

169.6600 

47  •  8603 

90 

.8189 

.2618 

187.9300 

49  •  2099 

95 

.1141 

.2431 

207  .  6000 

50.4618 

100 

•  4320 

.2256 

228.8030 

51.6247 

105 

4.7746 

.2094 

251-6330 

52.7036 

110 

S.I436 

.1944 

276.2380 

53.7055 

115 

5-54H 

.1805 

302.7330 

54-63SI 

120 

5  •  9693 

•  1675 

331-2880 

55-4985 

APPENDIX 
2  PER  CENT 


253 


n  years. 

I. 

II. 

III. 

IV. 

.0200 

.9804 

I  .0000 

.9804 

.0404 

.9612 

2.0200 

1.9416 

O6l2 

•9423 

3.0604 

2  .  8839 

.0824 

-9238 

4.  1216 

3.8077 

IO4I 

.9056 

5.2040 

4-7135 

1262 

.8880 

6.3081 

5.6014 

I487 

.8706 

7.4343 

6.4720 

.1717 

-8535 

8.5830 

7.3255 

I9SI 

.8368 

9-7546 

8.1622 

10 

2IQO 

.8203 

10.9497 

8.9826 

11 

2434 

.8043 

12.1687 

9-7868 

12 

2682 

.7885 

13.4121 

10-5753 

13 

2936 

•7730 

14.6803 

11.3484 

14 

•3IQS 

•  7579 

15-9739 

I2.IO62 

15 

•  3459 

•7430 

17-2934 

12.8493 

16 

•  3728 

.7284 

18.6393 

13-5777 

17 

.4002 

.7142 

2O.OI2I 

14.2919 

18 

.4282 

.7002 

21.4123 

14.9920 

19 

.4568 

.6864 

22.8406 

15-6785 

20 

•  4859 

.6730 

24.2974 

I6-35H 

21 

•5157 

.6598 

25-7833 

I7.OII2 

22 

.5460 

.6468 

27.2990 

17.6580 

23 

.5769 

.6342 

28.8450 

18.2922 

24 

.6084 

.6217 

30.4219 

I8.9I39 

25 

.6406 

•6095 

32.0303 

19.5235 

26 

•6734 

•  5976 

33.6709 

2O.  I2IO 

27 

.7069 

•5859 

35-3443 

20.7069 

28 

.7410 

•5744 

37-05I2 

2I.28I3 

29 

.7758 

•  5631 

38.7922 

21.8444 

30 

.8114 

•  SS2I 

40.5681 

22.3965 

31 

.8476 

.5412 

42-3794 

22.9377 

32 

.8845 

•5306 

44.2270 

23.4683 

33 

.9222 

.5202 

46.1116 

23.9886 

34 

.9607 

.5100 

48.0338 

24.4986 

35 

.9999 

.5000 

49-9945 

24.9986 

36 

•  0399 

.4902 

51.9944 

25.4888 

37 

.0807 

.4806 

54-0343 

25-9695 

38 

.1223 

.4712 

56.1149 

26.4406 

39 

.1647 

.4619 

58.2372 

26.9026 

40 

.2080 

•  4529 

60.4020 

27-3555 

41 

.2522 

.4440 

62.6100 

27-7995 

42 

.2972 

•4353 

64.8622 

28.2348 

43 

•  3432 

.4268 

67  •  1595 

28.66l6 

44 

•  3901 

.4184 

69.5027 

29.0800 

45 

-4379 

.4102 

71.8927 

29.4902 

46 

.4866 

.4022 

74.3306 

29.8923 

47 

•  5363 

•3943 

76.8172 

30.2866 

48 

•  5871 

•3865 

79-3535 

30.6731 

49 

.6388 

•3790 

81.9406 

31.0521 

50 

.6916 

•3715 

84.5794 

3I-4236 

55 

2.9717 

.3365 

98.5865 

33.1748 

60 

3.2810 

.3048 

114.0520 

34.7609 

65 

3.6225 

.2760 

131  .1250 

36.1973 

70 

3-9995 

.2500 

149.9780 

37.4986 

75 

4-4I58 

.2265 

170.7900 

38-6763 

80 

4.8754 

.2051 

193.7720 

39-7445 

85 

5-3828 

•  1858 

219.1400 

40-7111 

90 

5-9431 

.1683 

247-I570 

41-5869 

95 

6.5617 

.1524 

278.0850 

42.3800 

100 

7.2446 

.1380 

312.2320 

43.0984 

105 

7.9987 

.1250 

349.9300 

43.7489 

110 

8.8312 

.1132 

391.5590 

44.3382 

115 

9-7503 

.1026 

437-5I50 

44.87I9 

120 

10.7652 

.0929 

488.2580 

45-3554 

254 


APPENDIX 


i\  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

1.0250 

•9756 

I.  0000 

•Q756 

i  .  0506 

.95i8 

2.0250 

1.9274 

1.0769 

.9286 

3-0756 

2.8560 

i  .  1038 

.9060 

4-1525 

3-7620 

1.1314 

.8839 

5-2563 

4-6458 

i.  1597 

.8623 

6.3877 

5-5081 

1.1887 

-8413 

7-5474 

6  .  3494 

1.2184 

.8207 

8.7361 

7.1701 

i  .  2489 

.8007 

9-9545 

7.9709 

10 

i  .  2801 

.7812 

11-2034 

8.7521 

11 

1.3121 

.7621 

12.4835 

9-5142 

12 

1.3449 

•  7436 

I3-7956 

10.2578 

13 

I.378S 

.7254 

15.1404 

10.9832 

14 

1.4130 

.7077 

16.5190 

11.6909 

15 

1-4483 

.6905 

17.9319 

12.3814 

16 

I.484S 

.6736 

19.3802 

13.0550 

17 

1.5216 

.6572 

20.8647 

13-7122 

18 

1-5597 

.6412 

22.3863 

14-3534 

19 

1.5987 

•  6255 

23.9460 

14.9789 

20 

1.6386 

•  6103 

25-5447 

15-5892 

21 

1.6796 

•  5954 

27-1833 

16.1845 

22 

1.7216 

.5809 

28.8629 

16.7654 

23 

1.7646 

.5667 

30.5844 

17-3321 

24 

i  .  8087 

.5529 

32.3490 

17-8850 

25 

1.8539 

•  5394 

34-I578 

18.4244 

26 

1.9003 

-5262 

36.0117 

18.9506 

27 

1.9478 

-5134 

37-9120 

19.4640 

28 

1.9965 

.5009 

39.8598 

19.9649 

29 

2  .  0464 

.4887 

41.8563 

20.4535 

30 

2.0976 

.4767 

43.9027 

20.9303 

31 

2.  I5OO 

.4651 

46  .  0003 

21.3954 

32 

2  .  2038 

-4538 

48-1503 

21.8492 

33 

2.2589 

-4427 

50.3540 

22.2919 

34 

2.3153 

•4319 

52.6129 

22.7238 

35 

2.3732 

.4214 

54-9282 

23-1452 

36 

2.4325 

.4111 

57.3014 

23-5563 

37 

2-4933 

.4011 

59-7339 

23-9573 

38 

2-5557 

•  3913 

62.2273 

24-3486 

39 

2.6196 

•  3817 

64.7830 

24-7303 

40 

2.6851 

•  3724 

67  .4026 

25.1028 

41 

2.7522 

•  3633 

70.0876 

25.4661 

42 

2.8210 

-3545 

72.8398 

25.8206 

43 

2.8915 

•  3458 

75.6608 

26.1664 

44 

2.9638 

•3374 

78.5523 

26.5038 

45 

3-0379 

.3292 

81.5161 

26.8330 

46 

3-II39 

.3211 

84.5540 

27.1542 

47 

3-I9I7 

•  3133 

87.6679 

27-4675 

48 

3-27I5 

•3057 

90-8596 

27-7732 

49 

3-3533 

.2982 

94-I3H 

28.0714 

50 

3-4371 

.2909 

97-4843 

28.3623 

65 

3.8888 

•2571 

IIS-55I 

29.7140 

60 

4.3998 

.2273 

135.992 

30.9087 

65 

4.9780 

.  2009 

159.120 

31-963 

70 

5-6321 

•1775 

185.284 

32-898 

75 

6.3722 

.1569 

214.888 

33.645 

80 

7  .  2096 

•1387 

248.383 

34-452 

85 

8.1570 

.1226 

286.280 

35-096 

90 

9.2289 

.1084 

329.154 

35-666 

95 

10.4416 

.0958 

377.664 

36.171 

100 

11.8137 

.0846 

432.549 

36.614 

105 

13  .3661 

.0748 

494  .  644 

37-007 

110 

15.1226 

.0661 

564-902 

37-355 

115 

17.1098 

.0584 

644.392 

37.664 

120 

i9-358i 

•0517 

734-326 

37-934 

APPENDIX 


255 


3  PER  CENT 


n  years. 

I. 

II. 

III. 

rv. 

.0300 

.9709 

i  .0000 

.9709 

.0609 

.9426 

2  .0300 

1-9135 

.0927 

-9i5i 

3.0909 

2.8286 

•1255 

.8885 

4-1836 

3-7171 

-1593 

.8626 

5.309I 

4-5797 

.1941 

•8375 

6.4684 

5.4I72 

.2299 

.8131 

7-6625 

6.2303 

.2668 

.7894 

8.8923 

7-0197 

.3048 

.7664 

0-I59I 

7.7861 

10 

•3439 

•7441 

I  -4639 

8-5302 

11 

•3842 

.7224 

2-8075 

9-2526 

12 

-4258 

.7014 

4.1920 

9-9540 

13 

.4685 

.6810 

5-6178 

10.6350 

14 

.5126 

.6611 

7.0863 

i  i  .  2961 

16 

.S58o 

.6419 

8.5989 

H-9379 

16 

.6047 

.6232 

20.1569 

12.5611 

17 

-6528 

.6050 

21.7616 

13.1661 

18 

.7024 

•5874 

23.4144 

13-7535 

19 

•7535 

•  5703 

25-1169 

14-3238 

20 

.8061 

•5537 

26.8704 

14.8775 

21 
22 

-8603 
.9161 

•5375 
•  5219 

28.6765 
30-5368 

15-4150 
15-9369 

23 

•  9736 

.5067 

32.4529 

16.4436 

24 

.0328 

.4919 

34.4265 

16.9325 

25 

.0938 

•  4776 

36.4593 

17-4131 

26 

-1566 

•4637 

38.5530 

17.8768 

27 

.2213 

.4502 

40.7096 

18.3270 

28 

.2879 

•  4371 

42.9309 

18.7641 

29 

.3566 

•4243 

45.2I89 

19-1885 

30 

•4273 

.4120 

47-5754 

19.6004 

31 

•  5001 

.4000 

50.0027 

20.0004 

32 

•5751 

•  3883 

52.5028 

20.3888 

33 

•6523 

•  3770 

55.0778 

20.7658 

34 

•  7319 

.3660 

57-7302 

21.1318 

35 

.8139 

•  3554 

60.4621 

21.4872 

36 

.8983 

•  3450 

63-2759 

21.8323 

37 

.9852 

•  3350 

66.1742 

22.1672 

38 

3-0748 

•  3252 

69.1594 

22.4925 

39 

3-1670 

•  3158 

72-2342 

22.8082 

40 

3.2620 

.3066 

75-40I3 

23.1148 

41 

3-3599 

.2976 

78.6633 

23.4124 

42 

3-4607 

.2890 

82.0232 

23-7014 

43 

3-5645 

.2805 

85-4839 

23.9819 

44 

3-6715 

•  2724 

89-0484 

24.2543 

45 

3-7816 

.2644 

92.7199 

24.5187 

46 

3-8950 

•  2567 

96.5015 

24-7754 

47 

4.0119 

•  2493 

100.3965 

25.0247 

48 

4-1323 

.2420 

104.4084 

25.2667 

49 

4.2562 

•  2350 

108.5406 

25-50I7 

50 

4-3839 

.2281 

112.7969 

25-7298 

55 

5-0821 

.1968 

136.072 

26.7744 

60 

5-8916 

.1697 

163-053 

27.6756 

65 

6.8300 

.1464 

194-333 

28.452 

70 

7.9178 

.1263 

230.594 

29.123 

75 

9.1789 

.1089 

272.630 

29.702 

80 

10  .  6409 

.0940 

321.363 

30  .  201 

85 

12.3357 

.0811 

377-857 

30.701 

90 

14-3005 

.0699 

443-349 

31.002 

95 

16.5782 

.0603 

5I9-273 

3I-323 

100 

19.2186 

.0520 

607.288 

31-599 

105 

22.2797 

.0449 

709-323 

31-838 

110 

25.8282 

•  0387 

827.608 

32.043 

115 

29.9420 

.0334 

964.733 

32.220 

120 

34-7HO 

.0288 

1123.70 

32-373 

256 


APPENDIX 


3$  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

1.0350 

.9662 

I  .OOOO 

.9662 

1.0712 

•  9335 

2.0350 

1.8997 

I  .  1087 

.9019 

3  .  1062 

2.8016 

I-  I47S 

.8714 

4-2149 

3-6731 

1.1877 

.8420 

5-3625 

4-5i5i 

1.2293 

•  8135 

6-5502 

5-3286 

1.2723 

.7860 

7-7794 

6.1145 

1.3168 

•  7594 

9-0517 

6.8740 

1.3629 

-7337 

10.3685 

7.6077 

10 

1.4106 

.7089 

II-73I4 

8.3166 

11 

I  .4600 

.6849 

13-1420 

9.0016 

12 

1  .5111 

.6618 

14.6020 

9-6633 

13 

I  .  5640 

•  6394 

16.  1130 

10.3027 

14 

1.6187 

.6178 

17.6770 

10.9205 

15 

I-6753 

.5969 

19.2957 

II-5I74 

16 

I  -  7340 

•  5767 

20.9710 

12.0941 

17 

i  •  7947 

-5572 

22.7050 

12.6513 

18 

I.8S75 

-5384 

24-4997 

13.1897 

19 

1.9225 

.5202 

26.3572 

13  .  7098 

20 

1.9898 

.5026 

28.2797 

14.2124 

21 

2.0594 

-4856 

30.2695 

14.6980 

22 

2.1315 

.4692 

32.3289 

15.1671 

23 

2  .  2061 

•  4533 

34  .  4604 

15-6204 

24 

2  .  2833 

-4380 

36.6665 

16.0574 

25 
26 

2.3632 
2.4460 

-4231 
.4088 

38.9499 
4L3I3I 

16.4815 
16.8904 

27 

2.5316 

•  3950 

43-7591 

17.2854 

28 

2.6202 

-3817 

46  .  2906 

17.6670 

29 

2.7II9 

•  3687 

48.9108 

18.0358 

30 

2.8068 

•3563 

51.6227 

18.3920 

31 

2.9050 

•  3442 

54.4295 

18.7363 

32 

3.0067 

.3326 

57-3345 

19.0689 

33 

3.III9 

•  3213 

60.3412 

19-3902 

34 

3.2209 

•  3105 

63-4532 

19.7007 

35 

3.3336 

.3000 

66.6740 

20.0007 

36 

3.4503 

.2898 

70.0076 

20.2905 

37 

3-57Jo 

.2800 

73-4579 

20.5705 

38 

3.6960 

.2706 

77.0289 

20.8411 

39 

3-8254 

.2614 

80.7249 

21.1025 

40 

3-9593 

.2526 

84.5503 

2I.355I 

41 

4.0978 

.2440 

88.5095 

21.5991 

42 

4-2413 

•  2358 

92.6074 

21.8349 

43 

4.3897 

.2278 

96.8487 

22.0627 

44 

4-5433 

.2201 

101.2383 

22.2828 

45 

4.7024 

.2127 

105.7817 

22.4955 

46 

4.8669 

•  2055 

110.4840 

22.7009 

47 

5-0373 

.1985 

115-3510 

22.8994 

48 

5-2136 

.1918 

120.3883 

23.0912 

49 

5.396i 

.1853 

125  .6018 

23.2766 

50 

5.5849 

.1791 

130.9979 

23.4556 

55 

6.6331 

.1508 

160.947 

24.2641 

60 

7.8781 

.  1269 

196.517 

24-9447 

65 

9.3567 

.1069 

238.763 

25.5168 

70 

11.1128 

.O9OO 

288.938 

26.0004 

75 

13.1986 

•0758 

348.531 

26  .  4067 

80 

15.6757 

.0638 

4I9-307 

26.7488 

85 

18.6179 

-0537 

503-368 

27.0368 

90 

22.  1122 

.0452 

603  .  205 

27.2793 

95 

26.2623 

.0381 

721.780 

27.4798 

100 

31.1914 

.0321 

862.612 

27-6554 

105 

37-0456 

.0270 

1029.874 

27.8002 

110 

43.9986 

.O227 

1228.53 

27.9221 

115 

52.2565 

.Oigi 

1464.471 

28.0247 

120 

62.0643 

.Ol6l 

1744.69 

28.1111 

APPENDIX 


257 


4  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0400 

.9615 

I  .0000 

.9615 

.0861 

.9246 

2.0400 

1.8861 

.1249 

.8890 

3.1216 

2.7751 

.1699 

-8548 

4.2465 

3  •  6299 

.2167 

.8219 

5.4163 

4-4518 

.2653 

•  7903 

6  .  6330 

5.2421 

•3159 

•7599 

7-8983 

6.0021 

.3686 

.7307 

9-2142 

6.7327 

•4233 

.7026 

10.5828 

7-4353 

10 

.4802 

.6756 

12.0061 

8.1109 

11 

•  5395 

.6496 

13-4864 

8.7605 

12 

.6010 

.6246 

15.0258 

9-3851 

13 

-6651 

.6006 

16.6268 

9.9856 

14 

.7315 

•  5775 

18.2919 

10.5631 

15 

.8009 

•  5553 

20.0236 

11.1184 

16 

-8730 

•5339 

21.8245 

11.6523 

17 

-9479 

•  5134 

23-6975 

12.1657 

18 

.0258 

-4936 

25  •  6454 

12.6593 

19 

.1068 

•4746 

27.6712 

I3-I339 

20 

.1911 

-4564 

29.7781 

I3-5903 

21 

.2788 

•  4388 

31-9692 

14.0292 

22 

•  3699 

.4220 

34.2480 

14-45" 

23 

.4647 

•4057 

36.6179 

14.8568 

24 

•  5633 

•  3901 

39.0826 

15.2470 

25 

.6658 

•  3751 

41.6459 

15.6221 

26 

•  7725 

.3607 

44-3117 

15.9828 

27 

.8834 

•  3468 

47.0842 

16.3296 

28 

.9987 

•  3335 

49-9676 

16.6631 

29 

.1187 

.3207 

52.9663 

16.9837 

30 

•2434 

•3083 

56.0849 

17.2920 

31 

•  3731 

.2965 

59.3283 

17-5885 

32 

.5081 

.2851 

62.7015 

17.8736 

33 

.6484 

.2741 

66  .  2095 

18.1476 

34 

-7943 

.2636 

69-8579 

18.4112 

35 

.9461 

•  2534 

73-6522 

18.6646 

36 

.1039 

•  2437 

77.5983 

18.9083 

37 

.2681 

•  2343 

81.7022 

19.1426 

38 

4-4388 

.2253 

85-7903 

19-3679 

39 

4.6164 

.2166 

90.4091 

19-5845 

40 

4.8010 

.2083 

95-0255 

19.7928 

41 

4-9931 

.2003 

99.8265 

19-9931 

42 

5.1928 

.1926 

104.8200 

20.1856 

43 

5-4005 

•  1852 

110.0124 

20.3708 

44 

5-6165 

.1780 

115.4129 

20.5488 

45 

5.8412 

.1712 

121.0294 

20.7200 

46 

6.0748 

.1646 

126.8706 

20.8847 

47 

6.3178 

•1583 

132.9454 

21.0429 

48 

6.5705 

.1522 

139-2632 

21.1951 

49 

6-8333 

.1463 

I45-8337 

21.3415 

50 

7.1067 

.1407 

152.6671 

21.4822 

55 

8  .  6464 

•  1157 

191.159 

22.1086 

60 

10.5196 

•  0951 

237.991 

22.6235 

65 

12.7987 

.0781 

294.967 

23.0466 

70 

i5-57i6 

.0642 

364  .  290 

23-3945 

75 

iS-9453 

.0528 

448-642 

23.6281 

80 

23  .  0498 

.0434 

551-245 

23.9154 

85 

28.0436 

.0357 

676.090 

24.1085 

90 

34-H93 

.0293 

827.983 

24.2673 

95 

4i-5ii4 

.0241 

1012.785 

24-3977 

100 

50.5049 

.0198 

1237.622 

24-5050 

105 

61  .4470 

.0163 

I5ii-i75 

24.5931 

110 

74-7597 

•  0134 

1843.992 

24.6656 

115 

90-9566 

.0110 

2248.915 

24-7251 

120 

110.663 

.0090 

2741.558 

24.7741 

APPENDIX 


4l  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0450 

•  9569 

I.  0000 

•  9569 

.0920 

•  9157 

2.0450 

1.8727 

.1412 

•  8765 

3.1370 

2.7490 

•  1925 

.8386 

4.2782 

3.5875 

.2462 

.8022 

5-4707 

4-3900 

.3023 

.7679 

6.7169 

5-1579 

.3609 

.7348 

8.0192 

5-8927 

.4221 

.7032 

9.3800 

6-5959 

.4861 

.6729 

10.802  I 

7  .  2688 

10 

•553° 

.6439 

12.2882 

7-9125 

11 

.6229 

.6162 

13.8412 

8.5289 

12 

.6959 

.4897 

15.4640 

9.1186 

13 

.7722 

•  5643 

17.1599 

9.6829 

14 

.8519 

•  5400 

18.9321 

10.2229 

15 

•  9353 

•  5167 

20.7841 

10.7395 

16 

.0224 

•  4945 

22.7193 

11.2340 

17 

.1134 

•  4732 

24.7417 

11.7072 

18 

.2085 

.4528 

26.8551 

12.  1600 

19 

•  3079 

•4333 

29.0634 

12.5933 

20 

.4117 

.4146 

31.3716 

13-0079 

21 

.5202 

.3968 

33.7831 

13-4047 

22 

•  6337 

•  3797 

36.3034 

13.7844 

23 

.7522 

•  3634 

38.9370 

14.1478 

24 

.8760 

•  3477 

41.6892 

14-4955 

25 

3  -OOS4 

•  3327 

44.5652 

14.8282 

26 

3  •  1407 

.3184 

47.5706 

15.1466 

27 

3.2820 

.3047 

50.7113 

I5.45I3 

28 

3-4279 

.2916 

53-9933 

15-7429 

29 

3.5840 

.2790 

57-4230 

16.0219 

30 

3-7453 

.2670 

61.0071 

16.2889 

31 

3-9139 

•  2555 

64-7524 

16.5444 

32 

4.0900 

•  2445 

68.6662 

16.7889 

33 

4.2740 

.2340 

72.7562 

17.0229 

34 

4.4664 

.2239 

77.0303 

17-2468 

35 

4-6673 

.2143 

81.4966 

17.4610 

36 

4-8774 

.2050 

86.1640 

17.6660 

37 

5-0969 

.  1962 

91.0413 

17.8622 

38 

5-3262 

.1878 

96.1382 

18.0500 

39 

5.5659 

.1797 

101.4644 

18.  2297 

40 

5.8164 

.1719 

107.0303 

18.4016 

41 

6.0781 

.1645 

112.8467 

18.5661 

42 

6.3516 

•  1574 

118.9248 

18.7235 

43 

6.6374 

•  ISO? 

125.2764 

18.8742 

44 

6.9361 

.1442 

131-9138 

19.0184 

45 

7.2482 

.1380 

138.8500 

19-1563 

46 

7-5744 

.1320 

146.0982 

19  .  2884 

47 

7-9153 

.1263 

153.6726 

19.4147 

48 

8.2715 

.1209 

161.5879 

19.5356 

49 

8.6437 

•1157 

169.8594 

19-6513 

50 

9.0326 

.1107 

178.5030 

19.7620 

55 

11-2563 

.0888 

227.9180 

20.  2480 

60 

14.0274 

•  0713 

289.4980 

20.6380 

65 

17.4807 

.0572 

366.2380 

20.9509 

70 

21.7841 

•  0459 

461.8700 

21  .2O2I 

75 

27.1470 

•  0368 

581.2670 

21  .4118 

80 

33  -  8301 

.0296 

729.5580 

21.5653 

85 

42.1585 

.0237 

914.6330 

21.6951 

90 

52.5371 

.0190 

1145.2700 

21.7992 

95 

65.4708 

•  0153 

1432.6840 

21.8828 

100 

81.5885 

.0123 

1790.8600 

21-9499 

105 

101  .  674 

.0098 

2237.2000 

22.0036 

110 

126.704 

.0079 

2793.4300 

22.0468 

115 

157.897 

.0063 

3486.6000 

22.0815 

120 

196.768 

.0051 

4350.4000 

22.1093 

APPENDIX 


259 


5  PER  CENT 


«  years. 

I. 

II. 

III. 

IV. 

.0500 

•9524 

i  .0000 

•9524 

.1025 

.9070 

2.0500 

i  .  8594 

•  1576 

.8638 

3-I525 

2.7232 

•  2155 

.8227 

4.3101 

3-546o 

.2763 

.7835 

5-5256 

4-3295 

•  3401 

•7462 

6.8019 

5-0757 

.4071 

.7107 

8.1420 

5-7864 

•  4775 

.6768 

9-5491 

6.4632 

•  S5I3 

.6446 

11.0266 

7-1078 

10 

.6289 

.6139 

12.5779 

7.7217 

11 

•  7103 

•5847 

14.2068 

8.3064 

12 

•  7959 

-5568 

I5-917I 

8.8623 

13 

.8856 

.5303 

17.7130 

9.3936 

14 

•  9799 

•5051 

19-5986 

9.8986 

15 

.0789 

.4810 

21.5786 

10.3797 

16 

.1829 

.4581 

23-6575 

10.8378 

17 

.2920 

•4363 

25-8404 

11.2741 

18 

.4066 

.4155 

28.1324 

11.6896 

19 

.5270 

•  3957 

30.5300 

12.0853 

20 

•6533 

.3769 

33-o66o 

12.4622 

21 

.7860 

-3589 

35-7193 

12.8212 

22 

•  9253 

.3418 

38.5052 

13.1630 

23 

3-0715 

•  3256 

4I-4305 

13-4886 

24 

3-2251 

.3101 

44-5020 

13-7986 

25 

3-3864 

•  2953 

47.7271 

14.0939 

26 

3-5557 

.2812 

5i-"35 

14-3752 

27 
28 

3-7335 
3-9201 

.2678 
•  2551 

54-6691 
58.4026 

14.6430 
14.8981 

29 

4.1161 

•  2429 

62.3227 

15.1411 

30 

4-32I9 

.2314 

66.4388 

15.3725 

31 

4.538o 

.2204 

70.7608 

15-5928 

32 

4.7649 

.2099 

75-2988 

15-8027 

33 

5-0032 

.1999 

80.0638 

16.0025 

34 

5-2533 

.1904 

85  .  0670 

16.1929 

35 

5.5i6o 

.1813 

00.3203 

16.3742 

36 

5.79i8 

.1727 

95-8363 

16.5469 

37 

6.0814 

.1644 

101.6281 

16.7113 

38 

6-3855 

-1566 

107.7095 

16.8679 

39 

6.7048 

.1491 

114.0950 

17.0170 

40 

7.0400 

.1420 

120.7998 

I7.I59I 

41 

7.3920 

-1353 

127.8398 

17.2944 

42 

7.7616 

.1288 

135-2318 

17.4232 

43 

8.1497 

.1227 

142.9933 

17-5459 

44 

8-5572 

.1169 

151.1430 

17.6628 

45 

8.9850 

.1113 

139.7002 

17.7741 

46 

9  •  4343 

.1060 

168.6852 

17.8801 

47 

9.9060 

.1009 

178.1194 

17.9810 

48 

10.4013 

.0961 

188.0254 

18.0772 

49 

10.9213 

.0916 

198.4267 

18.1687 

50 

11.4674 

.0872 

209.3480 

18.2559 

55 

14-6356 

.0683 

272.7130 

18.6335 

60 

18.6792 

•  0535 

353-5840 

18.9293 

65 

23.8399 

.0419 

456.7980 

19.1191 

70 

30.4264 

.0329 

588.5290 

19-3427 

75 

38.8327 

-0257 

756.6540 

80 

49.5614 

.0202 

971.2290 

85 

63  •  2544 

.0158 

1245.0880 

90 

80.7304 

.0124 

1594.6100 

19.7523 

95 

103.035 

-0097 

2040  .  7000 

19.8058 

100 

I3I-50I 

.0076 

2610.0300 

19.8479 

105 

167.833 

.0060 

3336.6600 

19-8808 

110 

214.202 

.0047 

4264.0300 

19.9066 

115 

273-382 

-0037 

5447.6400 

19.9268 

120 

348.912 

.0029 

6958.2400 

19.9427 

260 


APPENDIX 


Si  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

•0550 

•  9479 

I.  0000 

•9479 

.1130 

•  8985 

2.0550 

1.8463 

.1742 

.8516 

3.1680 

2  .  6979 

.2388 

.8072 

4.3423 

3.5052 

.3070 

.7651 

5.5811 

4-2703 

.3788 

•  7252 

6.8881 

4-9955 

•4547 

.6854 

8.2669 

5-6830 

•5347 

.6516 

9.7216 

6.3346 

.6191 

.6176 

11.2563 

6.9522 

10 

.7081 

•  5854 

12.8754 

7.5376 

11 

.8021 

•  5549 

14.5835 

8.0925 

12 

.9012 

.5260 

16.3856 

8.6185 

13 

.0058 

.4986 

18.2868 

9.1171 

14 

.1161 

•  4726 

20.2926 

9-5896 

15 

•  2325 

•  4479 

22.4087 

10.0376 

16 

•  3553 

.4246 

24.6411 

10.4622 

17 

.4848 

.4024 

26.9964 

10.8646 

18 

.6215 

•  3815 

29.4812 

ii  .2461 

19 

.7656 

.3616 

32.1027 

11.6077 

20 

.9178 

•3427 

34.8683 

11.9504 

21 

3.0782 

•  3249 

37.7861 

12.2752 

22 

3-2275 

•  3079 

40.8643 

12.5832 

23 

3-4262 

•  2919 

44.1118 

12.8750 

24 

3-6146 

.2767 

47  •  538o 

13-1517 

25 

3-8134 

.2622 

51-1526 

13.4139 

26 

4-0231 

.2486 

54-9660 

13-6625 

27 

4.2444 

•  2356 

58.9891 

13.8981 

28 

4.4778 

.2233 

63.2335 

14.1214 

29 

4.7241 

.2117 

67.7114 

14.3331 

30 

4.9840 

.2006 

71-4355 

14-5337 

31 

5-2581 

.1902 

77.4194 

I4-7239 

32 

5-5473 

.1803 

82.6775 

14.9042 

33 

5-8524 

.1709 

88.2248 

I5-075I 

34 

6.1742 

.1620 

94.0771 

15-2370 

35 

6.5138 

•  1535 

100.2514 

15-3906 

36 

6.8721 

•  1455 

106.7652 

I5-536I 

37 

7-2501 

•  1379 

113-6373 

15.6740 

38 

7.6488 

•  1307 

120.8873 

15.8047 

39 

8.0695 

•  1239 

128.5361 

15.9287 

40 

8.5133 

•  1175 

136.6056 

16.0461 

41 

8.9815 

.1113 

145.1189 

16.1575 

42 

9-4755 

•  1055 

154-1005 

16.2630 

43 

9.9967 

.  IOOO 

163.5760 

16.3630 

44 

0.5465 

.0948 

173.5727 

16.4579 

45 

1.1266 

.0899 

184.1192 

16.5477 

46 

1.7385 

.0852 

I95.2457 

16.6329 

47 

2.3841 

.0807 

206.9842 

16.7137 

48 

3-0653 

.0765 

219-3684 

16.7902 

49 

3-7838 

.0725 

232.4336 

16.8628 

50 

14-5420 

.0688 

246.2175 

16.9315 

55 

19.0046 

.0526 

327-3563 

17-2251 

60 

24.8381 

.0403 

433.4200 

17.4498 

65 

32.4623 

.0308 

572.0364 

17.6216 

70 

43-4I50 

.0230 

771.1818 

17-7630 

75 

56.7414 

.0176 

1,013.4800 

17.8614 

80 

72.4703 

.0138 

1,299.4600 

17.9309 

85 

94.7152 

.0106 

1,703.9127 

17.9898 

90 

123.7883 

.0081 

2,232.5145 

18.0349 

95 

161.7855 

.0062 

2,923-3727 

18.0694 

100 

211.4463 

.0047 

3,826  .  2963 

18.0958 

105 

276.3503 

.0036 

5,006.3691 

18.1160 

110 

361.2768 

.0028 

6,550.4873 

18.1315 

115 

472.0413 

.0021 

8,564-3873 

18.1433 

120 

616.9357 

.0016 

11,198.8309 

18.1523 

APPENDIX 


261 


6  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0600 

•9434 

1.  0000 

•9434 

.1236 

.8900 

2.0600 

1.8334 

.1910 

.8396 

3.1836 

2  .  6730 

.2625 

.7921 

4-3746 

3-465I 

.3382 

•  7473 

5-6371 

4.2124 

.4185 

.7050 

6-9753 

4-9I73 

-5036 

-6651 

8.3938 

-5938 

.6274 

9.8975 

6.2098 

-6895 

•  5919 

11.4913 

6.8017 

10 

.7908 

.5584 

13.1808 

7.3601 

11 

.8983 

.5268 

14.9716 

7.8869 

12 

.0122 

-4970 

16.8699 

8.3838 

13 

.1329 

.4688 

18.882! 

8.8527 

14 

.2609 

•4423 

21  .OI5I 

9.2950 

15 

.3966 

•  4173 

23  .  2760 

9-7122 

16 

•  54°4 

.3936 

25.6725 

10.1059 

17 

.6928 

•  3714 

28.  2129 

10.4772 

18 

.8543 

•3503 

30.9057 

10.8276 

19 

.0256 

•  3305 

33.7600 

II.I58I 

20 

3-2071 

.3118 

36.7856 

11.4699 

21 

3  •  3996 

.2942 

39-9927 

I  I  .  7641 

22 

3-6035 

•  2775 

43-3923 

I2.04I6 

23 

3-8I97 

.2618 

46.9958 

12.3034 

24 

4.0489 

.2470 

50.8156 

12.5504 

25 

4.2919 

•  2330 

54.8645 

12.7834 

26 
27 

4-5494 
4-8223 

.2198 
.2074 

59-1564 
63.7058 

13-0032 
I3-2I05 

28 

5-IU7 

.1956 

68.5281 

13.4062 

29 

.1846 

73-6398 

I3-5907 

30 

5-7435 

.1741 

79.0582 

13-7648 

31 

6.0881 

.1643 

84.8017 

I3-929I 

32 

6.4534 

-I550 

90.8898 

14.0840 

33 

6.  8406 

.1462 

97-3432 

14.2302 

34 

7-2510 

•  1379 

104.1838 

14.3681 

35 

7.6861 

.1301 

III.4348 

14.4982 

36 

8.1473 

.1227 

II9.I2O9 

14.6210 

37 

8.6361 

.1158 

I27.268I 

14.7368 

38 

9-1543 

.1092 

135.9042 

14.8460 

39 

9-7035 

.1031 

145.0585 

14.9491 

40 

10.2857 

.0972 

154.7620 

15.0463 

41 

10.9029 

.0917 

165.0477 

I5-I380 

42 

11-5570 

.0865 

I75-9505 

I5-2245 

43 

2  .  2505 

.0816 

187.5076 

I5-3062 

44 

2.9855 

.0770 

199.7580 

I5-3832 

45 

3.7646 

.0727 

212-7435 

I5-4558 

46 

4  •  5905 

.0685 

226.5081 

I5-5244 

47 

.0647 

241.0985 

I5-5890 

48 

6-3939 

.0610 

256.5645 

15.6500 

49 

7-3775 

•  0575 

272.9584 

15.7076 

50 

8.4202 

•  0543 

290.3359 

15.7619 

55 

24  .  6507 

.0406 

394-I783 

15-9905 

60 

32.9883 

•  0303 

533-I383 

16.1611 

66 

44.1458 

.0226 

719.0966 

16.2891 

70 

59.0772 

.0169 

967.9533 

16.3845 

75 
80 

79  .  0587 
105.7985 

.0126 
.0095 

1,300.9783 
1,746.6416 

16.4558 
16.5091 

86 

141.5287 

.0071 

2,343-0450 

16.5489 

90 

189.4698 

-0053 

3,141.1633 

16.5787 

95 
100 

253.5538 
339.3125 

.0039 
.0029 

4,209.2300 
5,638.5416 

16.6009 
16.6175 

105 
110 
115 

454.0770 
607.6591 
813.1867 

.0022 
.0016 
.0012 

7,551.2833 
10,110.9850 
13,536.4450 

16.6299 
16.6392 
16.6461 

120 

1088.2280 

.0009 

18,120.4667 

16.6513 

262 


APPENDIX 


7  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

.0700 

•9346 

I.  0000 

.9328 

.1449 

.8736 

2.0700 

1.8043 

.2250 

.8163 

3.2142 

2.6228 

.3108 

.7629 

4.4400 

3.3857 

.4026 

•7130 

5.7514 

4.0986 

.5007 

.6663 

7.3529 

4.7657 

-6058 

.6227 

8.6542 

5.3886 

.7182 

.5820 

10.2600 

5.9700 

.8385 

•5439 

11.9786 

6.5143 

10 

.9671 

.5083 

13.8159 

7.0228 

11 

.1049 

•4751 

15.7843 

7-4971 

12 

.2522 

•4440 

17.8886 

7.94M 

13 

.4098 

.4150 

20.  1400 

8.3557 

14 

.5785 

.3878 

22.5500 

8.7442 

15 

•7590 

•3624 

25.1286 

9.1071 

16 

.9522 

•3387 

27.8886 

9  •  4457 

17 

3.IS88 

.3161 

30  .  8400 

9.7686 

18 

3.3800 

•  2959 

34.0000 

10.0571 

19 
20 

3.6165 
3.8697 

•2765 
.2584 

37.3786 

40.9528 

10.3343 
10.5928 

21 

4.1406 

•2415 

44.8657 

10.8343 

22 

4  •  4304 

.2257 

49.0057 

ii.  0600 

23 

4.740S 

.2109 

53-4343 

11.2714 

24 

5-0724 

.1971 

55-3200 

11.4685 

25 

5-4275 

.1842 

63.2500 

11.6528 

26 

5-8075 

.1722 

68.6786 

11.8242 

27 

6.2140 

.  1609 

74.4857 

n.9857 

28 

6  .  6490 

•1504 

80.7000 

12.1357 

29 

7.1144 

.1406 

87.3346 

12.2757 

30 

7.6124 

•1314 

94-4628 

12.4071 

31 

8.1452 

.1228 

102.0742 

12.5300 

32 

8-7154 

.1147 

110.2700 

12.6457 

33 

9.3255 

.  1072 

118.9500 

12.7528 

34 

9-9783 

.  IOO2 

128.2618 

12.8528 

35 

10.6768 

•0937 

138.2400 

12.9457 

36 

11.4241 

.0875 

148.9157 

13.0343 

37 

12.2239 

.O8l8 

160.3414 

I3-II57 

38 

13-0795 

.0765 

172.5642 

I3-I9I4 

39 

13.9950 

•0715 

185.6428 

13.2628 

40 

14.9747 

.0668 

199.6386 

13-3300 

41 

16.0230 

.0624 

214.6143 

13-3928 

42 

17.1446 

.0583 

230.6371 

13.4514 

43 

18.3448 

•0545 

247.7828 

13.5057 

44 

19.6290 

.0509 

266.1428 

I3-557I 

45 

21  .OO3O 

.0476 

285.7571 

13-6043 

46 

22.4332 

•0445 

306.1886 

I3.648S 

47 

24.0463 

.0416 

329.2328 

13-6900 

48 

25.7888 

.0387 

354.1257  „ 

13.7314 

49 

27.5306 

.0363 

379.0086 

13.7657 

50 

29-4577 

•0339 

406.5386 

13.8000 

55 

4I.3I62 

.0242 

575.9458 

13-9385 

60 

57.9482 

•0173 

813.5458 

i    .0371 

65 

81.2755 

-OI23 

1,146.7928 

i    .1085 

70 

113.9929 

.0088 

1,614.1844 

i    .1585 

75 

159.8823 

.OO62 

2,141.1757 

i    -1959 

80 

224.2440 

.0045 

2,269.7471 

I     .2200 

85 

3I4.5I38 

.0032 

3,160.6285 

I4.2385 

90 

44LI230 

.0023 

4,478.7682 

I4.25I4 

95 

6l8.7000 

.OOl6 

6,287-4714 

14.2614 

100 

867  .  7600 

.0011 

8,824.2857 

14.2685 

105 

I2I7.08I2 

.0008 

12,382.2855 

14.2728 

110 

1707.0235 

.0006 

17,372.5886 

14.2757 

115 

2394.1978 

.0004 

24,371.7642 

14.2785 

120 

3357.9923 

.0003 

34,188.5400 

14.2800 

APPENDIX 


263 


8  PER  CENT 


n  years. 

I. 

II. 

III. 

rv. 

.0800 

.9259 

1.  0000 

.9250 

.1664 
•  2597 

.8573 
.7938 

2.0800 
3-2463 

1.7825 
2.5762 

•  3605 

•  7350 

4-5062 

3.3112 

•  4693 

.6806 

5.8366 

3-9912 

.5869 

.6302 

7-3362 

4.6212 

•  7138 

.5840 

8.9225 

5-1987 

.8509 

•  5403 

10.6363 

5-7450 

.9990 

.5002 

12.4875 

6.2462 

10 

.1589 

.4632 

14.4862 

6.7087 

11 

•  3317 

.4289 

16  .  6463 

7-1375 

12 

.5182 

•  3971 

18.9775 

7-5350 

13 

.7196 

.3676 

21.4950 

7-9037 

14 

•  9372 

•3405 

24.2150 

8.2425 

15 

3-1722 

•  3152 

27-1525 

8.5587 

16 

3-4260 

.2919 

30.3250 

8.8513 

17 

3-7000 

.2703 

33-7500 

9.1200 

18 

3.9960 

.2502 

37-4500 

9-3712 

19 

4.3IS7 

•  2317 

41.4463 

9.6025 

20 

4.6610 

•2145 

45-7625 

9-8175 

21 

5-0339 

.1987 

50-4237 

10.0150 

22 

5.4366 

.1839 

55-4575 

IO.2OOO 

23 

5-8716 

•  1703 

60.8950 

IO.37OO 

24 

6.3413 

•  1577 

66.7663 

10.5275 

25 

6.8486 

.1460 

73-1075 

10.6737 

26 

7  •  3964 

.1352 

79.9800 

I0.8o87 

27 

7.9882 

.1252 

87-3525 

10-9337 

28 

8.6272 

•  II59 

95.3400 

n  .0500 

29 

9-3I74 

•  1073 

103-9675 

H-I575 

30 

10.0629 

.0994 

113.2862 

11.2562 

31 

10.8678 

.0920 

123.3475 

11.3487 

32 

H-737I 

.0852 

134-2138 

H-4337 

33 

12.6763 

•  0789 

145-9537 

11-5125 

34 

13  .  6904 

.0730 

158.6300 

11.5862 

35 

14-7853 

.0676 

172-3163 

II-6537 

36 

15-9684 

.0626 

187  .  1050 

11.7162 

37 

17.2460 

.0580 

203.0750 

H-7737 

38 

18.6249 

•0537 

220.3113 

11.8275 

39 

20.1159 

.0497 

238.9488 

II-8775 

40 

21.7250 

.0460 

259.0625 

11.9237 

41 

23.4630 

.0426 

280.7875 

11.9662 

42 

25.3400 

•  0395 

304.2500 

I  2  .  OO5O 

43 

27.3672 

•0365 

329.5900 

12.0425 

44 

29-5567 

•  0338 

356.9588 

12.0762 

45 

31-9213 

•  0313 

386.5163 

12.1075 

46 

34-4750 

.0290 

418.4375 

12.1362 

47 

37-2330 

.0269 

452.9125 

12.  1625 

48 

40.2117 

.0249 

490.1463 

I2.I875 

49 

43.4207 

.0230 

530.2588 

12.2112 

50 

46.9029 

.0213 

573.7863 

12.2325 

55 

68.9160 

•  0145 

848.9500 

12.3175 

60 

101  .  2605 

.0099 

1,253.2563 

12.3750 

65 

148.7849 

.0067 

1,847.3113 

12.4150 

70 

218.6150 

.0046 

2,720.  1875 

12.4412 

75 

321.2177 

.0031 

4,002.7213 

12.4600 

80 

471.9761 

.0021 

5,887  .  2013 

12.4725 

85 

693-4888 

.0014 

8,656.1100 

I2.48I2 

90 

1,018.9649 

.0010 

12,724.5613 

12.4862 

95 

1,497.1993 

.0007 

18,702.4913 

12.4900 

100 

2,199.8838 

.0005 

27,486.0475 

I2.492S 

105 

3,232.3656 

.0003 

40,392.0700 

12.4950 

110 

4,749.4130 

.0002 

59,355.1625 

12.4962 

115 

6,978.4677 

.OOOI 

87,218.3463 

12.4975 

120 

10,253.6792 

.OOOI 

128,158.4900 

12.4989 

264 


APPENDIX 


10  PER  CENT 


n  years. 

I. 

II. 

III. 

IV. 

I  .  IOOO 

.9091 

I.  0000 

0.908 

I.  2100 

.8264 

2.  IOOO 

1-735 

I.33IO 

•7513 

3-3100 

2.486 

1.4641 

.6830 

4.6410 

3.169 

I.6IOS 

.6209 

6.1050 

3-790 

I.77I6 

•5645 

7.7160 

4-354 

I.9487 

•5132 

9.4870 

4.867 

2.1436 

.4665 

11.4360 

5-334 

2.3580 

•4241 

13.5800 

5.758 

10 

2.5938 

•3855 

15.9380 

6.144 

11 

2.8531 

•3505 

18.5310 

6.494 

12 

3.1385 

.3186 

21.3850 

6.813 

13 

3-4523 

•2897 

24.5230 

7.102 

14 

3-7976 

.2633 

27.9760 

7.366 

15 

4-I773 

•2394 

31-7730 

7.605 

16 

4-S9SO 

.2176 

35.9500 

7-823 

17 

5-0545 

.1978 

40.5450 

8.021 

18 

5.5600 

.1799 

45.6000 

8.200 

19 

6.1160 

•1635 

51.1600 

8.364 

20 

6.7276 

.1486 

57.2760 

8.513 

21 

7.4004 

•I35I 

64  .  0040 

8.648 

22 

8.1404 

.1228 

71.4040 

8.771 

23 

8-9545 

.1117 

79.5450 

8.882 

24 

9  .  8500 

.1015 

88.5000 

8.984 

25 

10.8349 

.0923 

98.3490 

9.076 

26 

11.9184 

•0839 

109.1840 

9.160 

27 

13  .  1  103 

.0763 

121.  IO3O 

9.236 

28 

14.4213 

•  0693 

I34.2I30 

9.306 

29 

15.8634 

.0630 

148.6340 

9.369 

30 

17.4498 

•0573 

164.4980 

9.426 

31 

19.1948 

.0521 

181.9480 

9.478 

32 

21.1143 

.0474 

201.1430 

9.525 

33 

23.2257 

•0431 

222.2570 

9.568 

34 

25.5483 

.0391 

245.4830 

9.608 

35 

28.  1032 

•0356 

271.0320 

9.643 

36 

30.9135 

•0324 

299.1350 

9.675 

37 

34.0049 

.0294 

330.0490 

9.705 

38 

37.4054 

.0273 

364.0540 

9.726 

39 
40 

41.1460 
45-2605 

.0243 
.0221 

401.4600 
442.6050 

9.756 
9.778 

41 

49.7866 

.0201 

487  .  8660 

9.798 

42 

54.7655 

.0183 

537.6550 

9.816 

43 

60.2420 

.0166 

592.4200 

9.833 

44 

66.2662 

.0151 

652.6620 

9.848 

45 

72.8928 

•0137 

718.9280 

9.862 

46 

80.1822 

.0125 

791.8220 

9.874 

47 

88.2004 

.OII3 

872.0040 

9.886 

48 

97.0207 

.0103 

960.  2O7O 

9.896 

49 

106.7228 

.0094 

1,057.2280 

9.905 

60 

II7.3926 

.0085 

1,163.9260 

9.914 

55 

189.0668 

•0053 

I,880.6680 

9.946 

60 

304.4944 

•0033 

3,034.9440 

9.966 

65 

490.3932 

.OO2O 

4.893-9320 

9-979 

70 

789.7876 

.0013 

7,887.8760 

9.986 

75 

1,271.9648 

.OOOS 

12,709.6480 

9.991 

80 

2,048.5188 

.0005 

20,475.1880 

9-994 

85 

3,299.1742 

.0003 

32,981.7420 

9.996 

90 

5,313.3659 

.OOO2 

53,123.6590 

9-997 

95 

8,557-2549 

.0001 

85,562.5490 

9.998 

100 

13,781.6139 

.00007 

137,806.1390 

9.9992 

105 

22,195.5102 

.00005 

221,945.1020 

9  •  9994 

110 

35,746.1983 

.00003 

357,451.9830 

9.9996 

115 

57,569.8666 

.00002 

575,688.6660 

9-9997 

120 

92,717.0213 

.00001 

927,160.2130 

9.9998 

TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


N. 

o 

I 

2 

3 

j_| 

Diff. 

TOO 
101 

4321 

0434 
4751 

0868 

1734 

6038 

2166 
6466 

2598 
6894 

3029 
7321 

3461 
7748 

3891 

4H 

103 
103 

8600 
012837 

9026 
3259 

3680 

4100 

"0300  1 
4521 

•0724 
4940 

*"47 

*I57° 
5779 

*I993 
6197 

i! 

424 
420 

104 

7868 

8284 

8700 

9116 

9532 

9947 

*o36i 

*0775 

416 

105 

021189 

1603 

2016 

2428 

2841 

3252 

3664 

4°75 

4486 

4896 

412 

1  06 

53°6 

57  15 

6125 

6533 

6942 

735° 

7757 

8164 

8571 

8978 

408 

107 

9384 

9789 

0195 

0600 

1004 

1408 

•1812 

*22l6 

'2619 

*302I 

404 

108 
log 

033424 
7426 

7825 

4227 
8223 

4628 
8620 

5029 
9017 

543° 
9414 

583° 
9811 

6230 
*0207 

6629 

*0602 

7028 

•0998 

400 
397 

N. 

Diff. 

I 

Diff. 

434 

43 

87 

130 

i74 

217 

260 

304 

347 

391 

434 

433 

43 

87 

130 

*73 

217 

260 

3°3 

346 

433 

432 

43 

86 

130 

*73 

216 

259 

302 

346 

389 

432 

431 

43 

86 

129 

172 

216 

302 

345 

388 

431 

430 

43 

86 

129 

172 

215 

258 

301 

344 

387 

430 

430 

43 

86 

129 

172 

215 

257 

300 

343 

386 

429 

428 

43 

86 

128 

171 

214 

300 

342 

3«5 

428 

427 

43 

85 

128 

171 

214 

256 

299 

342 

384 

427 

426 

43 

85 

128 

170 

213 

256 

298 

341 

383 

426 

425 

A2A 

43 

gc 

128 

170 

213 

255 

298 

340 

383 

•$2 

425 

424 

4*4 

423 

42 

85 

127 

169 

212 

254 

297 

296 

339 

338 

o°* 

381 

423 

433 

42 

84 

127 

169 

211 

253 

295 

338 

380 

433 

431 

42 

84 

126 

168 

211 

253 

295 

337 

379 

421 

420 

42 

84 

126 

168 

2IO 

252 

294 

336 

378 

430 

09 
H 

9 

42 
42 

ss 

126 
125 

168 

167 

210 
209 

251 
251 

293 

293 

335 
334 

377 

376 

Si 

06 

42 

83 

"5 

167 

200 

250 

292 

334 

375 

417 

A 

4l6 

42 

83 

I25 

166 

20§ 

250 

291 

333 

374 

416 

4*5 

42 

83 

125 

166 

208 

249 

291 

332 

374 

415 

J 

4*4 

41 

83 

124 

166 

207 

248 

331 

373 

414 

413 

41 

83 

124 

165 

207 

248 

289 

330 

372 

413 

z 

412 

41 

82 

124 

165 

206 

247 

288 

330 

371 

413 

o 

4" 

41 

82 

123 

164 

206 

247 

288 

329 

370, 

4" 

410 

41 

82 

123 

164 

205 

246 

287 

328 

369 

410 

i 

9 

41 
41 

82 

82 

123 

122 

164 

163 

205 

204 

245 
245 

286 

286 

s 

367* 

409 
408 

m 

9 

41 
41 

81 
81 

122 
122 

163 
162 

204 
203 

244 
244 

285 
284 

326 

325 

366 
365 

$5 

Sj 

405 

41 

81 

122 

162 

203 

243 

284 

324 

365 

405 

404 

40 

81 

121 

162 

2O2 

242 

283 

323 

364 

404 

403 

40 

81 

121 

161 

202 

242 

322 

363 

403 

402 

40 

80 

121 

161 

2OI 

241 

281 

322 

362 

402 

401 

40 

80 

120 

160 

201 

241 

281 

321 

36i 

401 

400 

40 

80 

I2O 

160 

200 

240 

280 

320 

360 

400 

399 

40 

So 

120 

160 

200 

239 

279 

319 

359 

399 

39§ 

40 

80 

I  9 

159 

199 

239 

279 

3l8 

358 

398 

397 

40 

79 

i  9 

159 

238 

278 

3*8 

357 

397 

396 

40 

79 

i  9 

158 

IQ8 

238 

277 

317 

356 

396 

395 

40 

79 

198 

237 

3j6 

356 

395 

394 

39 

79 

i  8 

158 

197 

236 

276 

355 

394 

393 

39 

79 

i  8 

157 

197 

236 

275 

3H 

354 

393 

392 

39 

78 

i  8 

157 

196 

235 

274 

3H 

353 

392 

391 

39 

78 

i  7 

156 

196 

235 

274 

313 

352 

391 

390 

39 

78 

i  7 

156 

195 

234 

273 

312 

351 

390 

* 

39 

39 

78 

78 

"I 

156 
155 

195 
194 

233 

233 

272 
272 

3" 
310 

350 

349 

ill 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

265 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


Ill 

113 

«3 
114 

"§ 

116 


119 

130 

121 
122 
123 


I  "75 
4833 

^557 
2350 

5912 

9543 

m 

9905  "0258  *o6ii 
3772 


385 


2182  2576 


7426 
*0963 


5760 
9503 


8 


4540 
8442 

•2309 
6142 
9942 
3709 
7443 

*"45 

.!! 

5647 
9198 

*272I 
6215 


306 

3°5 
304 

303 
302 
303 

301 

300 
293 


895 

294 
294 
203 
292 
391 
290 

200 

2XQ 


2<i 


382 
28l 


8830 
*2694 

6524 
*0320 

4083 
7815 


6004 

9552 


6562 


348 

347 
347 
346 
345 
344 
343 
342 

341 
340 


338 
337 
336 
335 
334 
333 
332 
331 
330 
329 

a 

s 


321 
320 


316 


36o 

357 

355 


385 
384 


$ 

g 

8 

IS 
ill 


354 
353 


351 
350 


347 
Diff. 


266 


TABLE  VH.— LOGARITHMS  OF  NUMBERS. 


Ill 


096910 

100371 

3804 

7210 

110590 

"3943 


3852 
7105 

130334 
3539 
6721 
9879 

I430I5 


N.  |  Diff. 

¥ 

345 
344 
343 
342 

341 
34° 


tya 

130 
130 

1 20 

3 


127 

s 

126 
126 
125 
125 
124 
124 

124 
123 
123 


2091 
5510 
8903 

2270 
5611 

8926 

2216 

5481 
8722 

1939 
5133 
8303 
'1450 

4574 


2434 
5851 
9241 
2605 

5943 
9256 
2544 
5806 
9045 
2260 


•1763 
4885 


5196 


s 

935 

ass 
254 
aaa 

2.;  2 

2?  2 
251 

230 

250 

220 
22S 


225 
225 
224 
223 
223 
222 
221 
221 


2-.S 
217 

216 
zx6 

215 


275 

274 
27-1 

*73 

2-2 

271 

2-0 


afe 


2-1 
2'W 


250 

249 


9      Diff. 


267 


TABLE  VH.— LOGARITHMS  OF  NTMBERS. 


N. 

Diff. 

140 

146128 

6438 

6748 

7058 

7367  |  7676     7985       8294 

8603 

8911 

3°9 

141 

9219 

9527 

9*35 

•0142 

*0449 

•0756   *io6s  !  *I370 

•1676 

•1982 

307 

142 

152288 

2900 

3205 

3510 

3815     4120 

4424 

4728 

5032 

3°5 

143 
144 

BE 

§ 

5943 
8965 

9266 

65*9 

-=••  - 

6852  !  7154 
9866   *oi68 

•gg 

7759 
•0769 

8061 
*lo6S 

301 

161368 
4353 

1667 
4650 

1967 

2266 
5244 

2564 
5541 

2863     3161       3460 
5838     6134  i    6430 

3758 
6726 

4055 
7022 

299 
297 

1 

7317 
170262 
3186 

7613 

Si 

3769 

8203 
1141 

4060 

8497 
1434 
4351 

8792     9086       9380 
1726     2019  1    2311 
4641     4932  '    5222 

9674 
2603 
5512 

9968 
2895 

5802 

295 
293 
291 

150   176091 

6381 

6670  '  6959     7248     7536     7825       8113 

840! 

8689 

289 

151       8977 

9264       9552     9839  *t>326  :*04I3  *o699     *og86 

•1272 

**558 

287 

152    181844 

2129       2415     2700 

29S5  ;  327°     3555       3839 

4123 

4407 

285 

153 
154 

4691 
7521 

4975       5259     5542 

7803  !   8084    8366 

5825  ,  6108     6391       6674 
8647  ]  8928  i  9209       9490 

6956 
9771 

7239 
•0051 

283 
281 

155    190332 
156  1    3«5 
157       59°° 
158       8657 
159  ,201397 

0612 

f$ 

8932 
1670 

0892 
3681 
6453 
9206 

1943 

1171 
3959 
6729 
9481 
2216 

1451    i    1730    ,    2010         2289 
4237    I   4514    ,   4792          5069 
7005       72SI    1    7556          7832 

9755   "0029  "*o^o3     *0577 
2488  i  2761  j  3033  ;     3305 

4f 

3577 

2846 

& 

•1124 

3848 

3 
276 
274 
272 

N.       Diff.         i            2 

3 

4567 

8 

9 

Diff. 

3o6 

31               6l             92    i         22 

153    !      184            214 

245 

275 

306 

3P5 

-     31 

61 

92             22 

153          183    |         214 

244 

275 

305 

30 

61 

91 

22 

152 

182 

213 

243 

274 

304 

303 

3° 

61 
60 

91 

21 

152 

182 

212 

242 

273 

303 

302 
301 

3° 

60 

91 
90 

2O 

181 

211 

242 

241 

272 

271 

302 
301 

300 

3° 

60 

90 

20 

15° 

180 

210 

240 

270 

300 

31 

30 
30 

60 

60 

s 

20 
19 

ISO 

149 

179 
179 

209 
209 

3 

a 

g§ 

3 

3° 
30 

59 
59 

89 

19 

18 

149 
148 

178 
178 

208 

:•  ' 

238 
237 

267 
266 

3 

-/- 

295 

3° 

59 

89 

18 

148 

177 

207 

236 

266 

295 

2 

294 

29 

59 

88 

18 

147 

176 

206 

235 

265 

294 

^ 

293 

29 

59 

88 

17 

147 

176 

205 

234 

264 

293 

CU 

292 

29 

58 

88 

17 

146 

175 

204 

234 

263 

292 

291 

29 

58 

87 

16 

146 

175 

204 

233 

262 

291 

~ 

290 

29 

58 

87 

16 

145 

174 

203 

232 

261 

290 

Z 

289 

29 

58 

87 

16 

145 

173 

202 

231 

260 

289 

Z 

288 

29 

58 

86 

15 

144 

173 

202 

230 

259 

288 

P 

287 

29 

57 

86 

15 

144 

172 

201 

230 

258 

287 

tt 

286 

29 

57 

86 

14 

143 

172 

200 

229 

257 

286 

285 

29 

57 

86 

14 

143 

171 

20O 

228 

257 

285 

284 

28 

57 

85 

14 

142 

170 

199 

227 

256 

284 

o 

283 

28 

57 

85 

13 

142 

170 

198 

226 

255 

283 

0S 

282 

28 

56 

85 

13 

141 

169 

197 

226 

254 

282 

A 

281 

28 

56 

84 

12 

141 

169 

197 

225 

253 

281 

280 

28 

56 

84 

12 

140 

168 

196 

224 

252 

280 

£1 

28 
28 

t 

s 

12 

140 
139 

167 
167 

195 
195 

223 

222 

251 
250 

Si 

277 

28 

55 

83 

II 

139 

166 

194 

222 

249 

277 

276 

28 

55 

83 

IO 

138 

166 

193 

221 

248 

276 

275 

28 

55 

85 

10 

138 

165 

193 

220 

248 

275 

274 

27 

55 

82 

IO 

137 

164 

I92 

2I9 

247 

274 

273 

27 

55 

82 

09 

137 

164 

2X8 

246 

273 

272 

27 

54 

82 

°9 

136 

163 

190 

218 

245 

272 

271 

27 

54 

81 

108 

136 

163 

190 

217 

244 

271 

Diff. 

I 

*         3         4         5 

6 

7 

8 

9 

Diff. 

268 


TABLE  VIL— LOGARITHMS  OF  NTTMBERS. 


Diff. 


Diff. 


s 


3 

lit 

:^ 

^-.f 

250 

3 

245 


108 


3    1    4 


:?: 
-':- 
:.:- 
:.;.: 

:;:- 

--- 
132 
i°5  i     131 


269 


245  !  «7a 

244  \  «TI 


3 


:^ 


-;: 
-\;- 

*aa 

---- 

:;: 
-:: 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

1  80 
181 

255273 
7679 

5514 
7918 

5755 
8158 

5996 

6237 
8637 

6477 
8877 

6718 
9116 

6958 
9355 

7198 

9594 

7439 

9833 

241 
239 

183 

260071 

0310 

0548 

0787 

1263 

1501 

1739 

1976 

2214 

238 

183 

2451 

2688 

2925 

3162 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5054 

5290 

5525 

5996 

6232 

6467 

6702 

6937 

235 

185 

267172 

7406 

7641 

7875 

8110 

*8344 

8578 

88l2 

9046 

9279 

234 

1  86 

9513 

9746 

9980 

*02I3 

*0446 

*09I2 

*ii44 

*iS77 

*i6c>9 

233 

187 

271842 

2074 

2306 

2538 

2770 

3001 

3233 

3464 

3696 

3927 

232 

188 

4158 

4389 

4620 

4850 

5081 

53" 

5542 

5772 

6002 

6232 

230 

189 

6462 

6692 

6921 

7151 

7380 

7609 

7838 

8067 

8296 

8525 

229 

190 

278754 

8982 

9211 

9439 

9667 

9895 

*OI23 

*o35i 

*0578 

*o8o6 

228 

igi 
193 
193 

281033 
3301 

1261 
3527 
5782 

1488 
3753 
6007 

1715 
3979 
6232 

1942 

2169 

4431 
6681 

Is 

2622 

4882 
7130 

2849 
5I07 
7354 

3°75 
5332 
7578 

226 
225 

194 

7802 

8026 

8249 

8473 

8696 

8920 

9M3 

9366 

9589 

9812 

223 

195 

290035 

0257 

0480 

0702 

0925 

"47 

1369 

1591 

1813 

2034 

222 

196 
197 

4466 

2478 
4687 

2699 
4907 

2920 
5127 

5347 

3363 
5567 

3584 
5787 

3804 
6007 

4025 
6226 

4246 
6446 

221 
220 

198 
199 

6665 

8853 

6884 
9071 

7104 
9289 

7323 
9507 

7542 
9725 

7761 
9943 

7979 
*oi6i 

8198 
*o378 

8416 
*0595 

8635 
*o8i3 

2I9 

218 

200 

301030 

1247 

1464 

1681 

1898 

2114 

2331 

2547 

2764 

2980 

217 

201 
202 

3196 
5351 

3412 

5566 

3628 

578i 

5996 

4059 
6211 

4275 
6425 

4491 
6639 

6854 

4921 
7068 

5136 
7282 

216 

215 

203 
204 

7496 
9630 

7710 
9843 

7924 
*oos6 

8i37 
*0268 

8351 
*o48l 

8564 
*o693 

*8778 

8991 
*in8 

9204 
*I33° 

9417 

*I542 

213 

212 

N. 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

3 

24 

24 

48 
48 

72 
71 

96 
95 

20 

9 

i43 
143 

167 
167 

191 
190 

5 

3 

237 

24 

47 

71 

95 

142 

166 

237 

236 

24 

47 

71 

94 

8 

142 

165 

iSg 

236 

235 

24 

47 

71 

94 

8 

141 

165 

188 

235 

234 

23 

47 

70 

94 

7 

140 

164 

187 

234 

CD 

233 
233 

23 
23 

% 

70 
70 

93 
93 

I 

140 
139 

163 
162 

186 
186 

209 

233 
232 

H 

231 

23 

46 

69 

92 

6 

i39 

162 

i8s 

208 

231 

< 

230 

23 

46 

69 

92 

5 

138 

161 

184 

207 

230 

OH 

229 

23 

46 

69 

92 

5 

137 

160 

183 

206 

229 

s 

228 

23 

46 

68 

91 

4 

137 

160 

182 

205 

328 

^J 

227 

23 

45 

68 

91 

4 

136 

J59 

182 

204 

327 

£ 

226 

23 

45 

68 

90 

3 

158 

181 

203 

226 

O 

225 

23 

45 

68 

90 

3 

15 

158 

ISO 

203 

225 

224 

22 

45 

67 

2 

*34 

157 

179 

202 

224 

^ 

223 

22 

45 

67 

89 

2 

134 

156 

178 

201 

223 

0 

222 

22 

44 

67 

89 

I 

133 

155 

178 

200 

223 

221 

22 

44 

66 

88 

I 

133 

155 

177 

199 

221 

O 

22O 

22 

44 

66 

88 

0 

132 

154 

176 

198 

220 

04 

0k 

219 
3l8 

22 
22 

44 
44 

66 
65 

87 

10 
09 

131 
131 

153 

153 

175 

174 

;97 

III 

217 

22 

43 

65 

09 

130 

IS2 

174 

195 

317 

316 

22 

43 

65 

86 

08 

130 

151 

173 

194 

216 

215 

22 

43 

65 

86 

108 

129 

151 

172 

194 

215 

214 

21 

43 

64 

86 

107 

128 

15° 

171 

193 

214 

313 

21 

43 

64 

85 

107 

128 

149 

170 

192 

313 

212 

21 

42 

64 

85 

106 

127 

148 

170 

191 

313 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

270 


TABLE  VII.-LOGARITHMS  OF  NUMBERS. 


063 

146 


320 
322219 

4282 

6336 

838o 

330414 

332U8 

4454 

6460 

8456 

340444 

342423 

4392 

6353 

8305 

350248 

352I8J 

6026 
7935 
9835 
361728 
3612 
5488 
7356 
9216 


igg 
198 
197 
196 
195 
194 
193 
192 
191 
190 


4589 


0562 


8855 
oS4i 
28,7 
47\S 


*OO25  *O2I5 

1917 

;;-„ 
5675 

9587 


*0593 
2482 


9958 


"=0783 


*oi43 


3023 
5130 
7227 

1391 
3458 
55i6 
7563 
9601 
1630 


7659 
9650 
1632 

3606 
5570 
7525 
9472 
1410 
3339 
5260 
7172 
9076 


8473 
"=0328 


9456 


4077 
6131 
8176 

*02II 


2225 
4196 
6l57 

8110 


3910 
5834 
7744 
9646 


5301 
7169 
9030 


Diff. 

212 
211 
210 


271 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


N. 

0 

1 

2 

3 

Diff. 

235 

371068 

1253 

1437 

1622 

1806 

1991 

2175 

2360 

2544 

2728 

184 

236 
237 
238 

2912 

4748 
6577 

3096 
4932 
6759 

3280 
5H5 
6942 

3464 
5298 
7124 

3647 
548i 
7306 

3831 
5664 
7488 

Si 

7670 

4198 
6029 
7852 

4382 
6212 
8034 

4565 
6394 
8216 

184 
183 
182 

239 

8398 

8580 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

*0030 

181 

240 

380211 

0392 

0573 

0754 

°934 

1115 

1296 

1476 

1656 

1837 

181 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3097 

3277 

3456 

3636 

i  So 

242 

3815 

4174 

4353 

4533 

4712 

4891 

5070 

5249 

5428 

179 

243 
244 

5606 

739° 

5785 

5964 
7746 

6142 
7923 

6321 
8101 

6499 
8279 

6677 
8456 

6856 
8634 

7°34 
8811 

7212 
8989 

178 
178 

389166 

9343 

9520 

9875 

*005I 

*0228 

*04°5 

+0582 

*0739 

246 

390935 

1112 

1288 

1464 

164! 

1817 

1993 

2169 

2345 

2521 

176 

247 

2697 

2873 

3048 

3224 

34°o 

3575 

3751 

3926 

4101 

42/7 

176 

248 

4452 

4627 

4802 

4977 

5152 

5326 

5501 

5676 

5850 

6025 

175 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419 

7592 

7766 

174 

250 

397940 

8lI4 

8287 

8461 

8634 

8808 

4981 

9154 

*9328 

9501 

173 

251 

9674 

9847 

*0020 

*OI92 

*o365 

*o538 

*oS83 

*I228 

173 

252 

401401 

1573 

1745 

1917 

2089 

2261 

2433 

2605 

2777 

2949 

172 

253 
254 

3121 
4834 

3292 
5°°5 

3464 
5176 

3635 
5346 

3807 
5517 

5688 

4149 
5858 

4320 
6029 

4492 
6199 

4663 
6370 

171 
171 

1 

406540 
8240 

6710 
8410 

6881 
8579 

7051 

7221 
8918 

7391 
9087 

7561 
*9257 

7731 
9426 

7901 

9595 

8070 
9764 

170 
169 

9933 

*OI02 

*027I 

*o74o 

*o6o9 

*°777 

*ui4 

*I283 

*i4si 

160 

258 

411620 

1788 

1956 

2124 

2293 

246! 

2629 

2796 

2964 

3132 

168 

259 

3300 

3467 

3635 

3803 

397° 

4137 

4305 

4472 

4639 

4806 

167 

260 
261 
262 

4M973 
6641 
8301 

5T4° 

6807 
8467 

5307 

S 

5474 
7139 

*o?9? 

5641 
7306 
8964 

5808 
7472 
*9129 

5974 
7638 

*9295 

6141 
7804 
9460 

6308 
7970 
9625 

6474 
8i35 
9791 

167 
166 
165 

263 

9956 

*OI2I 

*02§6 

*o6i6 

*IIIO 

*I275 

*I439 

165 

2-64 

421604 

I768 

1933 

2097 

2261 

2426 

259° 

2754 

2918 

3082 

164 

N. 

Diff. 

I 

8 

9 

Diff. 

187 

19 

37 

56 

75 

94 

112 

131 

150 

168 

187 

186 

9 

37 

56 

74 

93 

12 

130 

149 

167 

1  86 

185 

37 

56 

74 

93 

II 

130 

148 

167 

185 

184 
183 

1 

37 
37 

55 
55 

74 
73 

92 
92 

10 

IO 

2 

3 

166 
165 

184 
183 

w 

182 

8 

36 

55 

73 

91 

09 

27 

146 

164 

182 

H 

181 

8 

36 

54 

72 

91 

09 

27 

145 

163 

181 

180 

8 

36 

54 

72 

90 

08 

26 

144 

162 

1  80 

I 

179 

8 

36 

54 

72 

90 

07 

25 

143 

161 

179 

178 

8 

36 

53 

89 

07 

25 

142 

160 

178 

J 

<; 

8 
g 

35 

53 

7i 

06 

106 

24 

142 

!59 

175 

8 

35 
35 

53 
53 

70 

88 

23 

140 

158 

175 

O 

174 

7 

35 

52 

7o 

87 

104 

22 

139 

157 

174 

H 

173 

7 

35 

52 

69 

87 

104 

21 

138 

156 

173 

172 

7 

34 

52 

69 

86 

103 

20 

138 

155 

172 

O 

7 

34 

68 

86 

103 

20 

137 

154 

171 

o, 
o 

170 

7 

34 

51 

68 

85 

IO2 

19 

136 

153 

170 

169 

7 

34 

51 

68 

85 

IOI 

18 

135 

152 

169 

cu 

1  68 

7 

34 

50 

67 

84 

101 

18 

134 

1  68 

167 

7 

33 

50 

67 

84 

100 

17 

134 

150 

167 

1  66 

7 

33 

50 

66 

83 

100 

16 

133 

149 

166 

165 

7 

33 

50 

66 

83 

99 

16 

132 

149 

165 

164 

16 

33 

49 

66 

82 

98 

15 

131 

148 

164 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


VII.— LOGARITHMS  OF  NUMBERS. 


274 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


TABLE  vn.— LOGARITHMS  OF  NUMBERS. 


N. 

O 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

380 

579784 
580925 
2063 

9898 
1039 

2177 

*OOI2 

"53 
2291 

*OI26 

1267 

2404 

*O24I 

1381 

2518 

*0355 
1495 
2631 

1608 

2745 

*o583 

*?§6 
2972 

*o8n 

as 

j 

3*3 

3199 

3312 

3426 

3539 

3652 

3765 

3879 

3992 

4105 

4218 

I 

384 

585^ 
6587 

4444 
5574 
6700 

4557 
5686 

6812 

4670 
5799 
6925 

4783 

5912 
7037 

4896 
6024 
7M9 

5009 
6137 
7262 

5122 
6250 
7374 

5235 
6362 
7486 

5348 
6475 

7599 

j 

387 

7711 

7823 

7935 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

I 

388 

8832 

8944 

9056 

^9167 

*9279 

*9391 

1*9726 

9838 

I 

389 

9950 

*oo6i 

*oi73 

*o6i9 

*073O 

*0953 

I 

39° 

591065 

1176 

1287 

1399 

1510 

1621 

1732 

1843 

1955 

2066 

I 

391 

2177 

2288 

2399 

2510 

2621 

2732 

2843 

2954 

3064 

3175 

I 

392 

3286 

3397 

3508 

3618 

3729 

3840 

3950 

4061 

4171 

4282 

I 

393 

4393 

4503 

4614 

4724 

4834 

4945 

5055 

5165 

5276 

I 

394 

5496 

5606 

5717 

5827 

5937 

6047 

6157 

6267 

6377 

6487 

I 

395 

596597 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7586 

1 

396 

7695 
8791 

7805 
8900 

79H 
9009 

8024 
9119 

9228 

8243 
9337 

8353 
9446 

9556 

8572 
9665 

8681 
9774 

109 

398 

9883 

9992 

*OIOI 

*02IO 

*03i9 

*0428 

*°537 

*o646 

*0755 

*oS64 

109 

399 

600973 

1082 

1191 

1299 

1408 

1517 

1625 

1734 

1843 

1951 

109 

400 

602060 

2169 

2277 

2386 

2494 

2603 

2711 

2819 

2928 

3036 

108 

401 

3U4 

3253 

336i 

3469 

3577 

3686 

3794 

3902 

4010 

4118 

108 

402 

4226 

4334 

4442 

4658 

4766 

4874 

4982 

5089 

5197 

108 

403 

5305 

5413 

5521 

5628 

5736 

5844 

5951 

6059 

6166 

6274 

108 

404 

6381 

6489 

6596 

6704 

6811 

6919 

7026 

7133 

7241 

7348 

107 

a 

607455 
8526 

7562 
8633 

8740 

is? 

7884 
8954 

7991 
9061 

8098 
*9l6? 

8205 
*9274 

8312 
938i 

8419 

9488 

107 
107 

409 

9594 
610660 
1723 

0767 
1829 

0873 
1936 

9914 
0979 
2042 

*002I 
2148 

*OI28 

1192 
2254 

?2o8 

2360 

1405 
2466 

*0447 
25/2 

*0554 
1617 
2678 

107 
06 

106 

10 

612784 

2890 

2996 

3102 

3207 

3313 

3419 

3525 

3630 

3736 

106 

II 

3842 

3947 

4°53 

4159 

4264 

4370 

4475 

458i 

4686 

4792 

106 

12 

4897 

5°°3 

5108 

5213 

5319 

5424 

5529 

5634 

5740 

5845 

105 

13 

5950 

6055 

6160 

6265 

6370 

6476 

6581 

6686 

6790 

6895 

105 

14 

7000 

7105 

7210 

7315 

7420 

7525 

7629 

7734 

7839 

7943 

105 

15 

618048 

8257 

8362 

8466 

8571 

8676 

8780 

SsV, 

^8989 

I05 

16 
17 

620^ 

0240 

9302 

0344 

9406 

0448 

95" 
0552 

9615 

0656 

9719 
0760 

9824 
0864 

9928 
0968 

104 
104 

18 

1176 

1280 

1384 

1488 

1592 

1695 

1799 

1903 

2007 

2110 

104 

419 

2214 

2318 

2421 

2525 

2628 

2732 

2835 

2939 

3042 

3146 

104 

N. 

Diff. 

I 

2 

3 

4 

5 

6 

7 

' 

9 

Diff. 

15 

12 

23 

35 

46 

58 

69 

81 

92 

104 

15 

M 

II 

23 

34 

46 

57 

68 

80 

91 

103 

14 

(0 

13 

11 

23 

34 

45 

57 

68 

79 

90 

IO2 

13 

H 

12 

II 

22 

34 

45 

56 

67 

78 

IOI 

12 

U 

ii 

II 

22 

33 

44 

56 

67 

78 

89 

IOO 

II 

O, 

10 

II 

22 

33 

44 

55 

66 

77 

88 

99 

IO 

109 

II 

22 

33 

44 

55 

65 

76 

87 

98 

09 

Q 

108 

II 

22 

32 

43 

54 

65 

76 

86 

97 

08 

(V 

107 

II 

21 

32 

43 

54 

64 

75 

86 

96 

07 

£ 

106 

II 

21 

32 

42 

53 

64 

74 

85 

95 

06 

105 

II 

21 

32 

42 

53 

63 

74 

84 

95 

i°5 

104 

IO 

21 

31 

42 

52 

62 

73 

83 

94 

104 

103 

10 

21 

31 

41 

52 

62 

72 

82 

93 

103 

Diff. 

•  I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

276 


TABLE  VII. -LOGARITHMS  OF  NUMBERS. 


TABLE;  vn.— LOGARITHMS  OF  NUMBERS. 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


711807 
2650 
349 1 
433« 

5l67 

716003 

6838 

7671 


345° 

724276 

5095 


9.05 

9974 

730782 

589 

732394 

3197 

3099 

4800 

5599 

736397 

7193 


9572 

740363 
1152 
1939 


6170 


4960 


70-iS 


9580 


*02I7 


1467 


3823 


3  !  4 


5  I 


8166 
9OI5 
9863 
0710 
1554 
2397 
3238 
4078 
4916 
5753 


7421 
8253 
9083 
9911 
0738 
1563 
2387 
3209 
4030 
4849 
5667 
6483 
7297 
8110 
8922 
9732 
*054° 
1347 
2152 


3759 
4560 
5359 
6i57 
6954 

8? 


0915 
1703 


4640 


5920 
6754 


1728 
2552 
3374 
4194 


8273 
9084 
9893 

*0702 

1508 
2313 

3"7 
39'9 
4720 


1073 

1860 
2647 
3431 
4215 


Diff. 


279 


VII.— LOGARITHMS  OF  NUMBERS. 


744293 
5075 
5855 
6634 
7412 

748i88 
8963 
9736 

750508 


51 12 

755875 
6636 

ll~ 
8912 

75<x'<*3 

760422 

1176 

1928 

2679 

763428 
4176 

4923 

5669 

6413 

767156 

7898 
8638 

9377 
770115 

770852 
1587 
2322 
3055 
37S6 

774517 
5246 
5974 
6701 
7427 


i 


4528 


4606 


osi? 


8934 


4684 


8576 


9008 


4762 


6859 


7179 

7955 

8731 
9504 

*0277 

1048 

1818 
2586 
3353 
4119 
4f3 
5646 


7927 
8685 
^9441 

0950 
1702 
2453 
3203 

3952 
4699 
5445 
6190 
6933 
-675 
8416 
9156 
9.894 
0631 
1367 

2102 
2835 
3567 
4298 
5028 
5756 
6483 
7209 

7934 


9659 
*°43i 

1202 
1972 
2740 
3506 
4272 
5036 

5799 
6560 
7320 


*Q347 


7082 
7823 
8564 
9303 

*0042 

0778 

1514 

2248 
2981 
3713 

4444 
5173 
5902 
6629 
7354 
8079 


9       Diff. 


280 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


Diff. 


8874 
9596 

780317 
1037 

781755 
2473 
3189 
39°4 
4617 

785330 
6041 
6751 
7460 


792392 
3092 


802774 
3457 
4139 
4821 
55°i 


809560 

810233 

0904 

1575 

2245 


Diff. 

73 
73 
71 
70 


0389 


4189 


2672 


8927 
9616 


9156 


9695 


*0029 


8730 
9452 
*oi?3 
0893 
1612 
2329 
3046 
376i 
4475 
5187 


7319 
8027 
8734 
9440 
*oi44 
0848 
1550 
2252 

2952 
3651 
4349 
5°45 


7i29 

7821 
85i3 
9203 

9892 
0580 
1266 
1952 
2637 
3321 
4003 
4685 
5365 
6044 
6723 
7400 
8076 
8751 
.9425 


9760 


454'-> 

53159 


8802  \  72 
9524  72 
'0245  72 

72 
72 
72 
7i 
TI 
71 

71 
7* 

n 
71 
71 

71 

TO 

TO 

70 

TO 
70 

70 

TO 

70 


"0215 
ogxa 

If',  JO 

3323 

3022 
37-'i 
4.,  is 
5JIS 

5s  1 1 


T800 


9961 

0648 
1335 

2705 

3389 

4071 
4753 
5433 
6112 

6790 

7467 
8143 
8818 
9492 
*oi65 
0837 
1508 
2178 
2847 


vn.— LOGARITHMS  OF  NUMBERS. 


N, 

O 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

650 

812913 

2980 

3°47 

3114 

3181 

3247 

33T4 

3381 

3448 

35H 

67 

65i 
652 

358i 
4248 

3648 
4314 

37M 
4381 

3781 

4447 

3848 
45M 

39i4 
4581 

398i 
4647 

4048 
47M 

4114 

4780 

4181 
4847 

67 
67 

653 
654 
655 

4913 

5578 
816241 

4980 
5644 
6308 

5046 
57" 
6374 

5H3 
5777 
6440 

5179 

5843 
6506 

5246 
591° 
65/3 

5312 
5976 
6639 

5378 
6042 
6705 

5445 

6lO9 

6771 

55U 
6175 
6838 

66 
66 
66 

656 

6904 

6970 

7036 

7102 

7169 

7235 

7301 

7367 

7433 

7499 

66 

657 

7565 

7631 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

66 

658 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

659 

8885 

8951 

9017 

9083 

9149 

9215 

9281 

9346 

9412 

9478 

66 

660 

819544 

9610 

9676 

9741 

9807 

9873 

9939 

*cxx>4 

*oo7o 

*oi36 

66 

661 
662 

820201 
0858 

0267 

°333 
0989 

°399 

0464 

0530 

°595 

0661 

0727 

°7% 

66 
66 

663 

I5M 

0924 
1579 

1645 

IO55 
1710 

1775 

1841 

1906 

1972 

2037 

2103 

65 

664 

2168 

2233 

2299 

2364 

2430 

2495 

2560 

2626 

2691 

2756 

65 

665 

822822 

2887 

2952 

3018 

3083 

3148 

3213 

3279 

3344 

34°9 

65 

666 

3474 

3539 

3605 

3670 

3735 

3800 

3865 

393° 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4451 

45i6 

458i 

4646 

4711 

65 

668 

4776 

4841 

4906 

4971 

5036 

5101 

5166 

5231 

5296 

536i 

65 

66g 

5426 

5491 

555° 

5621 

5686 

5751 

58i5 

5880 

5945 

6010 

65 

670 

826075 

6140 

62O4 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

65 

671 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7175 

7240 

73°5 

65 

672 
673 

7369 
8015 

7434 
8080 

7499 
8144 

7563 
8209 

7628 
8273 

7692 
8338 

7757 
8402 

7821 
8467 

7886 
8531 

7951 
8595 

i 

674 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9J75 

9239 

64 

676 

829304 
9947 

*9368 

9432 
*oo75 

9497 
*oi39 

956i 

*O2O4 

9625 
*0268 

9690 
•6333 

9754 
*o396 

9818 
*o46o 

9882 
*Q525 

64 
64 

67778 

830589 

0653 

0717 

0781 

0845 

0909 

°973 

1037 

1102 

1166 

64 

679 

1870 

1934 

1998 

2062 

2126 

sc 

2253 

2317 

2381 

2445 

64 

680 

832509 

2573 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3083 

64 

681 
682 

3M7 
3784 

3211 

3848 

3275 

3338 
3975 

3402 

4°39 

3466 

3530 

3593 

3657 

372i 
4357 

64 
64 

683 

4421 

4484 

4548 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

3 

684 

5056 

5120 

5183 

5247 

53io 

5373 

5437 

55oo 

5564 

5627 

63 

685 

835691 

5754 

5817 

5881 

5944 

OOOy 

6071 

6i34 

6197 

6261 

63 

686 

6324 

6387 

6451 

6514 

6577 

6641 

6704 

6767 

6830 

6894 

63 

687 

6957 

7020 

7083 

7146 

7210 

7273 

7399 

7462 

7525 

63 

688 

7588 

7652 

7715 

7778 

7841 

7904 

7967 

8030 

8093 

8i56 

63 

689 

8219 

8282 

8345 

8408 

8471 

8534 

8597 

8660 

8723 

8786 

63 

690 

838849 

8912 

8975 

9038 

9101 

9164 

9227 

9289 

9352 

9415 

63 

691 

9478 

9541 

9604 

9667 

9729 

9792 

9855 

9918 

9981 

*oo43 

63 

692 

840106 

0169 

0232 

0294 

0357 

0420 

0482 

°545 

0608 

0671 

63 

693 

°733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

694 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

1860 

1922 

63 

695 

841985 

2047 

2172 

2235 

2297 

2360 

2422 

2484 

2547 

62 

696 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

62 

697 

3233 

3295 

3357 

3420 

3482 

3544 

3606 

3669 

3731 

3793 

62 

698 

3855 

39i8 

3980 

4042 

4104 

4166 

4229 

4291 

4353 

4415 

62 

699 

4477 

4539 

4601 

4664 

4726 

4788 

4850 

4912 

4974 

5036 

62 

N. 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

{ft 

H 

67 

7 

13 

20 

27 

34 

40 

47 

54 

60 

67 

ft, 

66 

7 

13 

20 

26 

33 

40 

46 

53 

59 

66 

65 

7 

13 

20 

26 

33 

39 

46 

52 

59 

65 

o 

64 

6 

13 

19 

26 

32 

38 

45 

5i 

58 

64 

£ 

63 

6 

13 

19 

25 

32 

38 

44 

50 

63 

EH 

62 

6 

12 

19 

25 

3i 

37 

43 

50 

56 

62 

Diff. 

I 

a 

3 

4 

5 

6 

7 

8 

9 

Diff. 

282 


TABLE  VII— LOGARITHMS  OF  NUMBERS. 


851258 
1870 
2480 
3090 
3698 

854306 
4913 
5519 
6124 
6729 

857332 
7935 
8537 
9138 


0937 
1534 
2131 
2728 

863323 
3917 
45" 
5104 


6878 
7467 
8056 
8644 

869232 
9818 

870404 
0989 
1573 

872156 
2739 
3321 
3902 
4482 


Diff. 


2389 


8497 


9525 

*OIII 

0696 


7326 
7943 
8559 


0401 
1014 
1625 
2236 
2846 
3455 
4063 
4670 
5277 
5882 
6487 
7091 


0697 
1295 


4274 
4867 
5459 
6051 
6642 
7232 
7821 
8409 
8997 

9584 
*oi70 
0755 
1339 
1923 
2506 
3088 
3669 
4250 
4830 


9056 
9642 


9173 
9760 

*°345 


3262 


4424 
5°°3 


283 


TABLE   VII. -LOGARITHMS  OF  NUMBERS. 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

75° 
751 

875061 
5640 

1st" 

5177 

5756 

5235 
5813 

5293 

5871 

5351 

5929 

54°9 

5987 

5466 
6045 

6102 

5582 
6160 

§ 

752 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

58 

753 

6795 

6853 

6910 

6968 

7026 

7083 

7141 

7199 

7256 

73  14 

58 

754 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

58 

877947 

8004 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

57 

756 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

8981 

9°39 

57 

757 

9096 

9153 

9211 

9268 

9325 

9383 

9440 

9497 

*oif5 

9612 

57 

758 

9669 

9726 

9784 

9841 

9898 

9956 

*OOI3 

+0070 

*oi8s 

57 

759 

880242 

0299 

0356 

0413 

0471 

0528 

0585 

0642 

0699 

0756 

57 

760 
761 

1385 

0871 

1442 

0928 
1499 

0985 
1556 

1042 
1613 

1099 
1670 

1156 
1727 

1213 

1784 

1271 

1841 

1328 

1898 

57 
57 

762 

1955 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

763 

2525 

258l 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3037 

57 

764 

3093 

3150 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

3605 

57 

8 

883661 
4229 

3718 
4285 

3775 
4342 

3832 
4399 

3888 

4455 

3945 
4512 

4002 
4569 

4059 
4625 

4115 

4172 
4739 

57 
57 

767 

4795 

4852 

4909 

4965 

5022 

5078 

5135 

5192 

5248 

53°5 

57 

768 
769 

5926 

54'8 
5983 

5474 
6039 

5531 
6096 

5587 
6152 

5644 
6209 

5700 
6265 

5757 
6321 

5813 
6378 

5870 
6434 

H 

770 

886491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

771 

7°54 

7167 

7223 

7280 

7336 

7392 

7449 

7505 

756i 

56 

772 

7674 

7730 

7786 

7842 

7898 

8011 

8067 

8123 

56 

773 
774 

III 

8i79 
8741 
889302 
9862 

8236 

8/97 
9358 
9918 

8292 
8853 
9414 
9974 

8348 
8909 
9470 

8404 
8965 
9526 
*ooS6 

8460 
9021 
9582 
*oi4i 

9077 
*o138 

8573 
9134 
9694 

8629 
9190 

975° 
*°3°9 

8685 
9246 
9806 
*o365 

1 

777 
778 

890421 
0980 

°477 

0533 

*osiS 

0645 

0700 

0756 

0812 

0868 

0924 

$ 

779 

1537 

1593 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

56 

780 

892095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

2595 

56 

78i 

2651 

2707 

2762 

2818 

2873 

2929 

2985 

3040 

3096 

3*51 

56 

782 

3207 

3262 

3373 

3429 

3484 

3540 

3595 

3651 

37°6 

56 

783 

3762 

3817 

3873 

3928 

3984 

4039 

4094 

415° 

4205 

4261 

55 

784 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

55 

785 

894870 

4925 

4980 

5036 

5091 

5M6 

5201 

5257 

5312 

5367 

55 

786 
787 

5423 

5975 

5478 
6030 

6085 

5588 
6140 

6i95 

5699 
6251 

5809 
6361 

5864 
6416 

5920 
6471 

55 
55 

788 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 

55 

789 

7077 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7572 

55 

790 

897627 

7682 

7737 

7792 

7847 

7902 

7957 

8012 

8067 

8122 

55 

791 

8176 

8231 

8286 

8341 

8396 

8451 

8506 

8561 

8615 

8670 

55 

792 

8/25 

8780 

8835 

8890 

8944 

8999 

9°54 

9109 

9164 

9218 

55 

793 
794 

9273 
9821 

9875 

993° 

9437 
9985 

9492 
*oo39 

*9547 

9602 

9656 

*0203 

9711 

9766 

*03I2 

55 
55 

III 

900367 
0913 

0422 
0968 

0476 

1022 

0531 
1077 

0586 
1131 

0640 
1186 

0695 
1240 

0749 
1295 

0804 
J349 

0859 

1404 

55 
55 

797 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

54 

798 
799 

2003 
2547 

2057 
2601 

2112 
2655 

2166 
2710 

2221 
2764 

2275 
2818 

2873 

2384 

2927 

a 

2492 
3036 

54 
54 

N. 

Diff. 

' 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

t 

57 

6 

II 

17 

23 

29 

34 

40 

46 

51 

57 

04 

56 

6 

11 

17 

22 

28 

34 

39 

45 

50 

56 

- 

55 

6 

II 

17 

22 

28 

33 

39 

44 

50 

55 

M 

cu 

54 

5 

II 

16 

22 

27 

32 

38 

43 

49 

54 

Diff. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

284 


TABLE;  vn.— LOGARITHMS  OF  NUMBERS. 


834 


849 


903090 
3633 
4174 
4716 
5256 

905796 
6335 
6874 
7411 

7949 

908485 
9021 
9556 

910091 
0624 

911158 
1690 

2222 

2753 

3284 

913814 


5400 
5927 
916454 
6980 
7506 
8030 
8555 


9601 
20123 
0645 


921686 


6927 


I  4 


S712 


3416 
3958 

4499 

558o 
6119 
6658 
7196 

7734 


9342 
9877 
0411 
0944 
1477 
2009 
2541 
3072 
3602 


6243 
6770 
7295 
7820 
8345 


9392 
9914 
0436 
0958 
1478 
1998 
2518 
3°37 
3555 
4072 


5106 
5621 
6i37 


7678 
8191 
8703 
92I5 


3470 

4OI2 

4553 
5094 
5634 
6i73 
6712 
7250 

9396 
9930 
0464 
0998 
1530 
2063 
2594 
3125 
3655 
4184 
4713 
5241 
5769 
6296 
6822 
7348 
7873 
8397 
8921 

9444 
9967 
0489 
1010 
1530 
2050 
2570 
3089 
3607 
4124 

4641 
5157 


6702 
7216 
7730 
8242 


4607 
5148 
5688 
6227 
6766 
7304 
7841 
8378 
8914 
9449 
9984 
0518 


2116 
2647 
3178 
3708 

4237 
4766 
5294 
5822 
6349 
6875 
7400 
7925 
8450 
8973 
9496 
*ooig 
0541 
1062 
1582 

2102 
2622 


4I76 

4693 
5209 
5725 
6240 


Diff. 


285 


VII.— LOGARITHMS  OF  NUMBERS. 


857 


I  862 
863 


929419 
9930 


931966 
2474 


3487 

3993 

934498 


864  |   6514 


884 


8019 
8520 


939519 

940018 

0516 


942008 


944483 
4976 
5469 


946943 
7434 
7924 
8413 
8902 

94939° 
9878 

950365 
0851 
1338 

951823 
2308 
2792 
3276 
3760 


65f,4 
;<,'/> 
75"S 


8570 


4038 


1386 


9572 
*oo83 
0592 

1102 

1610 
21 18 

2626 

3639 

4145 

4650 

5154 


9623 

*oi34 


9674 

*o:85 
0694 


4-M» 


4680 


2986 


7267 
77°9 
8269 
8770 
9270 

9769 
0267 

07'<5 
1263 
1760 
2256 


7189 

767<) 
Sif.S 
S6.S7 
9146 

9634 

*OI2I 


3518 


0796 


8     9   Diff.l 


4953 
5457 
596o 
6463 
6966 
7468 
7969 
8470 
8970 
9469 
9968 
0467 
0964 
1462 
1958 
2455 
2950 
3445 
3939 
4433 
4927 
5419 


286 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


TABLE  VII.— LOGARITHMS  OF  NUMBERS. 


980003 
0458 


1819 

982271 
2723 

llll 

4077 

984527 


S3 

986772 
7219 
7666 
8113 
8559 

989005 
945° 
9895 

990339 
0783 

991226 
1669 


3877 

4317 
4757 
5196 

995635 
6074 
65:2 
6949 
7386 

997823 
8259 
8695 
9J3I 
9565 


01 5$ 


8648 


6599 


7 


*0028 

0472 
0916 


*0072 

0516 

0960 


336 


9672 
*oii7 
0561 
1004 

1448 
1890 
2333 

2774 

32;'-) 

4097 

4557 
4977 
5416 

5854 
020; 
6731 
7168 
7605 
8041 
8477 


7998 
8454 
8911 
9366 
9821 
0276 
0730 
1184 
1637 


2543 
2994 
3446 
3897 
4347 
4797 
5247 
5696 
6144 
6593 
7040 
7488 
7934 
8381 
8826 
9272 


0605 
1049 
1492 

1935 
2377 
2819 
3260 
37°i 
4141 

5021 

5898 
6337 

6774 
7212 
7648 
§085 
8521 


8500 
8956 
9412 
9867 

0776 
1229 
1683 
2135 
2588 
3040 
3491 
3942 
4392 
4842 
5292 


6637 
7085 
7532 
7979 
8425 
8871 

9761 

*0206 

0650 
1093 

1536 

1979 

2421 

2863 
3304 

3745 
4185 
4625 
5065 
55°4 
5942 
6380 
6818 
7255 
7692 
8129 
8564 
9000 
9435 


*0250 

0694 


8135 
8591 
9047 
9503 
9958 
0412 
0867 
1320 

1773 

2226 


3130 

3581 

4032 
4482 

4932 


6279 

7 '75 

7',  22 
§068 
B5I4 
8960 

94<15 
9850 


1625 
2067 
2509 
2951 
3392 
3833 
4273 
4713 
5152 
5591 
6030 
6468 
6^06 
7343 


8652 


9522 
9957 


Q, 

45  1        5          9         14         18 

23  1       27 

32 

36 

41 

45 

• 

44l        4 

9 

13 

18 

22   1           26 

3i 

35 

40 

44 

ft, 

43 

4 

9  '       13 

17 

22 

26 

3° 

34 

39 

43 

Diff. 

I 

2 

3 

4         5 

6 

7 

8 

9 

Diff. 

288 


VII.— LOGARITHMS  OF  NUMBERS. 


INDEX 


ARTICLE  PAGE 

Accessibility  of  standing  timber,  definition  of 175  178 

Account,  general  outlay  and  income,  in  forestry 131  118 

profit  and  loss,  in  forestry 131  n8 

trading  and  profit  and  loss,  in  forestry 131  n8 

Accounts,  capital 20  n 

capital,  in  forestry 131  j  18 

cost 25  16 

cost,  in  forestry 92  70 

economic,  forms  of,  in  forestry 132  1 19 

outlay  and  income 21  12 

profit  and  loss 21  12 

proprietary 19  n 

proprietary,  in  forestry 91  69 

specific 19  ii 

specific,  in  forestry,  forms  for 131  117 

valuation 54  35 

valuation,  versus  specific  accounts 19  1 1 

valuation,  in  forestry 110  85 

Accumulations  of  compound  interest,  effect  of  rate  of  interest  upon ...  51  30 

Additions  to  capital 73  49 

Administration  expenses 100  75 

Esthetic  values 147  138 

Age,  economic 145  137 

Agricultural  land,  expectation  value  of 237  230 

sale  value  of 238  230 

soils,  definition  of 225  226 

value,  timber  as  an 239  230 

versus  forest  values  of  land 236  229 

Agriculture  versus  forestry  as  a  source  of  livelihood 232  227 

All-aged  stand,  taxes  paid  upon 158  148 

Amortization,  definition  of 173  1 73 

Annual  profits 40  23 

Anticipation  of  continuous  profits 126  107 

Anticipated  profits  on  young  timber 124  106 

Application  of  methods  of  computing  depreciation  in  lumbering 178  185 

Appraisal  in  lumbering 120  102 

of  damages,  principles  underlying 133  120 

timber  left  after  logging 107  83 

value 60  38 

291 


2Q2  INDEX 

ARTICLE  PAGE 

Appraisals,  field 213  216 

of  stumpage,  price  basis  in 172  170 

value 171  169 

stumpage,  reports 224  222 

stumpage,  increasing  future  values  as  basis  of 195  206 

principle  underlying 18  10 

Appraised  value 17  10 

effect  of  capital  value  upon 70  45 

Assets,  appreciation  of 73  50 

in  balance  sheet 73  46 

re- valuation  of 73  48 

valuation  accounts  for 19  n 

Average  logging  costs,  the  basis  of  stumpage  appraisals 175  179 

Balance  sheet 73  48 

economic,  in  forestry 132  119 

in  forestry 131  117 

problem  of  the 73  46 

specific,  in  forestry 120  100 

Bark -boring  beetles 202  211 

Basis  for  profits  in  lumbering,  investment 178  184 

of  comparison  of  agricultural  with  forest  values  of  land 236  2  29 

damages,  expectation  or  capital  value 139  1 29 

sale  value 138*  128 

stumpage  appraisals,  increasing  future  values  as 195  206 

value  of  forests,  income  as Ill  85 

Bonds,  timber,  interest  on,  as  a  carrying  charge 181  192 

on  standing  timber 96  72 

Boxes  and  crates,  use  of  wood  for 189  199 

Brown-tail  moth 202  211 

Brush  burning,  cost  of 100  74 

Building,  use  of  wood  for 189  199 

Business  investments,  rate  of  interest  for 47  28 

of  forest  production,  the 90  68 

venture 28  17 

Cancellation  of  classification  of  lands  for  forest  taxation 166  164 

of  cost  of  land  from  sale  of  timber 107  83 

Capital 12  6 

additions  to 73  49 

deductions  from 73  49 

definition  of 12  7 

working 24  15 

account,  nature  of 20  12 

accounts 20  n 

in  forestry 131  1 18 

and  income,  distinction  in  timber  property.  .  .  .  : 156  145 

expenditures,  in  forestry 93  71 


INDEX  293 

ARTICLE   PAGE 

Capital,  invested  in  forest  production,  earning  power  of 129     in 

investment,  stumpage  as  a 176     180 

returns  on 31      jg 

stock 28      17 

value,  a  basis  of  damages 139     z  2g 

definition  of 62      39 

effect  of  rate  of  interest  on 66      42 

effect  upon  appraised  value 70      45 


sale  value. . 


44 


independence  of  past  outlay  or  cost 

of  forest  soil 116  92 

future  sums 77  54 

perpetual  rentals 86  62 

temporary  annual  rentals 81  58 

intermittent  rentals 83  60 

time  element  in 65  42 

uncertainty  of 67  43 

values,  inflation  of 71  45 

Capitalist,  function  of  the 13  7 

Capitalization,  regulation  of 72  46 

Capitalized  expenses,  as  additions  to  capital 73  50 

income  value,  definition  of 62  40 

rental  value,  definition  of 62  40 

value,  definition  of 62  39 

Carrying  charge,  interest  as  a 36  22 

charges  versus  profits  on  stumpage 181  191 

Chestnut  bark  disease 203  211 

Classification  of  costs  in  forest  production 104  76 

land 235  229 

land,  national  forest  policy  in 166  164 

lands,  cancellation  of,  in  forest  taxation 250  238 

Clear  lumber 184  196 

Cleared  land  versus  stump  land 240  231 

Clearing  stump  lands,  cost  of 241  232 

Climate,  agricultural 228  226 

Climatic  injuries  as  a  physical  risk 204  211 

Closeness  of  utilization 186  197 

as  affecting  timber  estimates 217  2 19 

Combined  capital  tax  and  income  tax 163  154 

Commutation  tax  on  forest  property,  Massachusetts 166  163 

Comparison  of  agricultural  and  forest  values  of  land 236  229 

agriculture  with  forestry  as  a  source  of  livelihood 232  227 

bare  forest  soil  with  agricultural  soil 248  237 

costs,  profits  and  stumpage  value  by  overturn  methods,  diagram  III  177  184 

results  of  simple  and  compound  interest 49  28 

taxes  on  different  forests,  Table  II 168  148 

forest  rent  versus  soil  rent 161  151 

total  forest  values  with  value  of  agricultural  soil 249  237 


294  INDEX 

ARTICLE  PAGE 

Compensation,  in  damages 133  120 

Competition,  effect  of 7  4 

Compound  interest,  definition  of 16  8 

comparison  of  results  with  simple  interest 49  28 

uses  of 16  9 

Computation  of  taxes  under  general  property  tax 164  157 

Connecticut,  taxation  of  forests  in 166  161 

Constitutional  provisions  of  general  property  tax 166  165 

Continuous  forest  production,  profits  from 125  107 

value  of  forest  property  for 113  88 

profits,  anticipation  of 126  107 

Contractors'  profits  in  logging 177  182 

Contracts,  long  term,  revision  of  stumpage  values  in 196  207 

to  provide  against  damages 140  132 

Control  of  risks,  insurance 209  213 

private  measures 211  214 

public  measures 210  213 

Conversion  of  intermittent  into  annual  rentals 88  65 

Correction  factor  in  timber  estimating 222  221 

Cost  accounts 25  16 

in  forestry 92  70 

and  value,  essential  difference  between 58  37 

as  a  basis  of  value 56  35 

interest  as  a 36  20 

of  assets,  addition  of  annual  deficit  to 73  48 

brush  burning 100  74 

clearing  stump  lands 241  232 

growing  timber,  calculation  of 105  77 

investments  in  standing  timber 106  79 

labor,  in  lumbering 190  201 

many-aged  forests 108  83 

milling 174  177 

producing  a  normal  forest 109  84 

raw  material,  stumpage  as  a 176  181 

re-establishing  protective  cover,  as  basis  of  damages 146  138 

replacement,  as  basis  of  damages 137  126 

restoration,  in  damages 133  121 

slash  disposal 100  74 

transportation,  elements  in 98  73 

past.    Independence  of  capital  value  and 68  44 

Costs,  formulae  for 243 

future,  effect  on  value 10  5 

of  forestry  compared  with  destructive  lumbering 107  81 

logging 175  178 

in  forest  production,  classification  of 104  76 

specific 25  16 

Cruisers,  timber 218  219 

Current  annual  forest  per  cent 129  114 


INDEX  295 

ARTICLE  PAGE 

Damage  by  fire,  character  of 136  I22 

to  forest  soil 143  z 35 

forest  property,  elements  of 133  1 22 

immature  timber,  partial  loss 141  I32 

total  loss • 142  133 

many-aged  stands 146  ^j 

merchantable  timber 140  131 

single  trees 144  I36 

soil,  expressed  in  extra  initial  costs 142  134 

watersheds 146  137 

Damages,  basis  of;  cost  of  replacement 137  126 

expectation  or  capital  value,  a  basis  of 139  129 

formulae  for 247 

increased  future  prices  not  a  basis  of 139  130 

principles  underlying  appraisal  of 133  1 20 

punitive 147  I39 

rate  of  interest  as  affecting 139  131 

sale  value  a  basis  of 138  128 

Deductions  from  capital 73  49 

Deferred  profits 41  23 

Definition  of  symbols 241 

Defoliating  insects 202  211 

Demand 5  2 

Depreciation  as  a  cost  of  milling 174  177 

a  deduction  from  capital 73  49 

an  expense  in  logging 175  179 

definition  of 173  1 73 

formulas  for 247 

fund 173  173 

Hunter's  formula 173  175 

methods  of  reckoning 173  174 

necessity  for,  in  accounting 20  1 1 

Destructive  lumbering,  costs  of,  compared  with  forestry 107  81 

profits  in 122  105 

value  of  forest  property  for 112  86 

Deterioration  of  merchantable  timber,  damages  due  to 140  132 

standing  timber 185  196 

Determination  of  legitimate  profits  in  lumbering 177  181 

Diagram  I,  periods  required  for  $i  to  multiply 51  31 

II,  method  of  balancing  future  costs  and  income 116  93 

III,  comparison  of  stumpage  values,  by  overturn  methods 177  184 

Diaporthe  parasitica 203  211 

Difference  between  cost  and  value,  essential 58  37 

Discount 16  8 

factor,  definition  of 74  53 

Discrimination  against  forest  values  in  land  classification 246  236 

in  favor  of  forest  values  in  land  classificatibn 247  236 

Diseases,  fungous 203  211 


296  INDEX 

ARTICXE  PAGE 

Disposition  of  income 30  17 

Distinction  between  capital  and  income  in  timber  property 166  145 

Dividends,  interest  versus 32  18 

Douglas  fir,  deterioration  of,  in  Washington  State 185  196 

Doyle  log  rule '. 179  187 

Doyle-Scribner  log  rule 179  187 

Earning  power  of  capital  invested  in  forest  production 129  in 

an  investment 121  105 

Economic  accounts,  forms  of,  in  forestry 132  119 

age  of  a  stand 146  137 

balance  sheet,  in  forestry 132  1 19 

comparison,  in  accounting 73  52 

factors,  in  classification  of  soil  as  agricultural 231  227 

forecast,  in  forestry 120  101 

opportunity 27  16 

per  cent  earned  on  forest  investments 129  112 

profits 120  104 

Effect  of  capital  value  upon  appraised  value 70  45 

sale  value 69  44 

deferred  income  upon  rate  of  interest 48  28 

general  property  tax  on  forest  production 165  158 

present  condition  of  forest  upon  choice  of  methods  of  taxation. . .  .  168  147 

rate  of  interest  upon  accumulations  of  compound  interest 51  30 

interest  upon  capital  value 66  42 

risks  on  the  business  of  forest  production 212  214 

substitutes  on  wood  prices 189  198 

taxes  on  property  values 153  143 

Effort  or  outlay 6  3 

Elements  of  damage  to  forest  property 134  122 

value  for  forest  land 243  233 

Enterpriser,  definition  of  term 39  23 

Enterpriser's  profit  or  gain 39  23 

Entrepreneur,  definition  of  term 39  23 

Equality  of  taxation 153  143 

Errors  in  methods  of  timber  estimating 219  220 

Estimation  of  standing  timber 215  218 

Even-aged  forest,  value  for  any  year 115  90 

for  any  year,  formula 116  95 

just  previous  to  cutting 114  89 

stand,  taxes  paid  upon 168  148 

Exchange 29  17 

Expectation  value,  a  basis  of  damages 139  1 29 

definition  of 62  39 

of  agricultural  soil 237  230 

forest  soil 116  92 

future  series 77  54 

perpetual  rentals 86  62 


INDEX  297 
ARTICLE    PAGE 

Expectation  value,  of  temporary  annual  rentals 81  58 

intermittent  rentals 83  60 

Expenses,  future,  appraisal  of 64  41 

included  in  outlay  and  income  accounts 21  12 

investments  versus 22  13 

or  temporary  outlay  in  forestry 94  71 

versus  value 57  35 

Exploitation  of  land  purchasers 234  229 

Factors  affecting  future  value  of  forest  products 182  195 

determining  stumpage  prices 170  167 

Federal  income  tax  law,  with  reference  to  cost  accounts  for  parcels  of 

land 181  193 

Field  appraisals,  scope  of 213  216 

methods  of  timber  estimating 218  219 

Final  income,  definition  of 61  38 

Financial  risks 208  212 

definition  of 198  208 

Finished  products,  prices  of 8  4 

Fire  as  a  moral  risk 207  212 

physical  risk 200  209 

killed  timber,  damages  for 140  131 

lines,  cost  of 100  75 

public  measures  for  control  of 210  213 

Fire-resistance  in  trees 200  209 

Forced  sales 17  10 

Forecast,  economic,  in  forestry 120  101 

or  prospectus,  in  accounting 73  51 

Forest  of  50  acres,  taxes  paid  upon 168  148 

investments,  rate  of  interest  on 62  32 

land  bare  of  timber,  taxation  of 166  161 

tax 160  150 

per  cent,  current  annual 129  114 

mean  annual 129  114 

production,  classification  of  costs  in 104  76 

continuous,  profits  from 125  107 

value  of  forest  property  for 113  88 

earning  power  of  capital  invested  in 129  in 

effect  of  general  property  tax  upon 165  158 

risks  upon ••••  212  2I4 

versus  lumbering 

products,  changes  in  prices  of 188  197 

future  value  of I82  IQ5 

property,  elements  of  damage  to 134  122 

sale  value  of 245  235 

tax I69  149 

tax  reform  for I66  l6° 

value,  for  destructive  lumbering H2  8o 


298  INDEX 

'  ARTICLE  PAGE 

Forest  rent,  theory  of 166  146 

versus  soil  rent,  comparison  of  taxes  on 161  151 

soil,  damage  to 143  135 

value  of 116  92 

young  timber  as  part  of  value  of 244  234 

Forest  statics,  definition  of 120  100 

taxation  in  Connecticut 166  161 

Massachusetts 166  161 

Pennsylvania 166  161 

problem  of  interest  in 167  146 

valuation,  summary  of  formulae  in 243 

values,  discrimination  against,  in  land  classification 246  236 

in  favor  of,  in  land  classification 247  236 

utilization,  business  of 90  68 

versus  agricultural  values  of  land 236  229 

Forestry,  interest  rates  in,  compared  with  other  investments 63  33 

versus  agriculture  as  a  source  of  livelihood 232  227 

Forms  for  specific  accounts  in  forestry 131  117 

economic  accounts  in  forestry 132  119 

Formulae  for  costs 243 

damages 247 

depreciation 247 

geometric  series 248 

geometric  series,  discussion  of 80  57 

interest  earned 246 

profits 246 

stumpage  values 248 

values 244 

in  forest  valuation,  summary 243 

of  compound  interest,  summary 240 

Fumes,  as  a  physical  risk 205  212 

Fungous  diseases,  as  a  physical  risk 203  211 

Future  crops  of  trees,  as  a  measure  of  damage  to  soil. 143  135 

expenses,  appraisal  of 64  41 

in  taxation 162  152 

income  as  a  basis  of  value 61  38 

operating  costs,  effect  on  stumpage  values 190  201 

prices  and  values,  uncertainty  of 63  41 

as  a  basis  of  damages 139  130 

supply  of  timber,  as  a  local  factor  in  stumpage  appraisals 193  204 

transportation  facilities,  in  stumpage  appraisals 191  202 

value  of  forest  products 182  195 

temporary  annual  rentals 79  56 

intermittent  rentals 82  59 

or  cost  of  single  sums 76  53 

values,  increasing,  as  basis  of  stumpage  appraisals 195  206 


INDEX  299 

ARTICLE  PAGE 

Gauging  of  risks 199  209 

General  outlay  and  income  account  in  forestry 131  118 

price  changes  as  affecting  stumpage  values 187  196 

property  tax,  the 164  144 

effect  of,  upon  forest  production 165  158 

on  forest  property 164  155 

Geometric  series,  formulae  for '. 248 

formulae  for,  discussion  of 80  57 

Grades  of  lumber,  prices  for,  as  basis  of  stumpage  appraisals 172  171 

Grading  logs 223  222 

Grass,  inflammability 200  210 

Growing  stock,  even-aged,  value  of 119  98 

many-aged,  value  of 119  99 

Growth  in  volume  of  stand 183  195 

Gypsy  moth 202  211 

Hardwood  litter,  inflammability 200  210 

Hazard,  in  risks,  definition  of 199  209 

Humus  or  duff,  inflammability 200  210 

Hunter's  formula  for  depreciation  and  interest 173  176 

Immature  timber,  partial  loss,  damages 141  132 

total  loss,  damages 142  133 

Improvement  in  quality  of  products 184  196 

Improvements,  permanent  investment  in 96  73 

Income 26  16 

accounts,  outlay  and 21  12 

as  the  basis  of  value  of  forests Ill  85 

disposition  of 30  17 

future,  as  a  basis  of  value 61  38 

interest  as 37  22 

or  products  tax 162  152 

potential 73  48 

secondary,  from  forests Ill  86 

tax,  combined  with  capital  tax 163  154 

law,  federal,  with  relation  to  cost  accounts  by  parcels 181  193 

on 16°  HI 

timber  lands 162  152 

value,  capitalized,  definition  of 62  40 

definition  of 62  40 

versus  profits 42  24 

Increase  in  stumpage  value,  rate  of 194  2°4 

Increased  future  prices  not  a  basis  of  damages 139  130 

Increasing  future  values  as  basis  of  stumpage  appraisals 195  206 

Independence  of  capital  value  and  past  outlay  or  cost 44 

Industries  and  markets,  local,  effect  on  stumpage  appraisals 192  203 

Inflation  of  capital  values 71  45 

Influence  of  personality  on  the  rate  of  interest 44      26 


300  INDEX 

ARTICLE  PAGE 

Influences  determining  the  rate  of  interest 43  26 

Injurious  fumes,  as  a  physical  risk 205  212 

Insects,  as  a  physical  risk 202  211 

Installation,  period  of,  in  business 23  14 

Insurance  on  timber 209  213 

Intention  to  grow  timber,  influence  in  appraising  damages  to  young 

timber 138  129 

Interest 14  7 

as  a  cost 36  20 

as  distinguishing  income  from  enterprisers'  profits 42  25 

as  income 37  22 

cannot  be  deducted  from  income;  federal  income  tax 162  153 

charges,  as  an  expense 103  76 

compound 16  8 

definition  of 14  8 

earned,  formulae  for 246 

not  a  cost  in  determining  legitimate  profit  in  lumbering 178  185 

on  bonds,  as  a  carrying  charge 181  192 

problem  of,  the 36  20 

in  forest  taxation 157  146 

rate  of,  the 38  22 

rate  of,  for  business  investments 47  28 

rates  in  forestry,  comparison  with  other  investments 53  33 

rates  paid  by  savings  banks 53  33 

simple 16  9 

versus  dividends 32  18 

versus  value 57  35 

Inventory,  definition  of 55  35 

Investments,  business,  rate  of  interest  in 47  28 

forest,  rate  of  interest  in 52  32 

in  lumbering,  status  of,  resembling  forest  production 120  103 

or  permanent  outlay  in  forestry 93  71 

other  than  forestry,  comparison  of  interest  rates  with  forestry 53  33 

versus  expenses 22  13 

Investment  basis  for  profits  in  lumbering 178  184 

in  standing  timber,  total  cost  of ' 106  79 

seed  trees. 107  82 

total 24  14 

Irregular  income,  value  of  many-aged  forests  producing 118  97 

Labor,  cost  of,  in  lumbering 190  201 

Land,  agricultural  versus  forest  values  of 236  229 

classification 236  229 

national  forest  policy  in 260  238 

investment  in 95  71 

prices  for 9  5 

purchasers,  exploitation  of 234  229 

tax,  forest 160  150 


INDEX  301 

ARTICLE  PAGE 

Landscape  gardening  as  basis  for  appraising  damages 147  139 

Larch  sawfly 202  211 

Legitimate  profits  in  lumbering  —  overturn  method 177  181 

versus  speculative  value 67  43 

Liabilities,  in  balance  sheet 73  46 

Liability,  in  risks,  definition  of 199  209 

Life  insurance,  interest  rates  in 53  33 

Limitation  of  opportunity 50  29 

Loans 14  8 

Local  factors  in  stumpage  appraisals;  industries  and  markets 192  203 

stumpage  appraisals;  future  supply  of  timber 193  204 

stumpage  appraisals;  future  transportation  facilities 191  202 

revenue,  maintenance  of,  in  forest  taxation 166  161 

Logarithms,  use  of 78  55 

Log  grades 223  222 

markets 172  1 70 

rules 216  218 

Logging,  definition  of 90  68 

Logging  chance,  definition  of 213  216 

costs  and  profit 175  178 

effect  on  fire  hazard 200  2 10 

Logs,  price  of,  as  basis  of  stumpage  appraisal 172  170 

Long  term  contracts,  revision  of  stumpage  values  in 196  207 

Loss  in  value  of  entire  property,  a  basis  of  damages 138  128 

of  income  in  damages 133  121 

Lumbering,  destructive,  costs  of,  compared  with  forestry 107  81 

status  of  investment  in,  resembling  forest  production 120  103 

versus  forest  production 90  68 

Maintenance  of  local  revenue,  in  forest  taxation 166  161 

Many-aged  forests,  cost  of 108  83 

producing  irregular  income,  value  of 118  97 

regular  income,  value  of 117  96 

stands,  damage  to 145  137 

Map,  reconnaissance 214  217 

Marketing  of  wind-thrown  timber 201  211 

Markets,  local,  effect  on  stumpage  appraisals 192  203 

Massachusetts,  taxation  of  forests  in 166  161 

Mean  annual  forest  per  cent 129  1 14 

Merchantable  timber,  definition  of 167  166 

damages  to 140  131 

taxation  of 166  162 

Methods  of  taxation,  effect  of  present  condition  of  forest  upon 158  147 

timber  estimating,  field 218  219 

Mill  prices,  as  a  basis  of  stumpage  appraisals 172  171 

Mill  run  prices,  in  stumpage  appraisals 172  172 

Milling,  definition  of 90  68 

costs  and  profits 174  i?7 


302  INDEX 

ARTICLE  PAGE 

Mixed  stands,  stumpage  value  for  different  species  in 180  188 

Money,  definition  of 2  i 

fluctuating  values  of,  as  affecting  rate  of  interest 46  27 

Monopoly,  effect  of,  upon  prices  and  values 7  4 

Moral  risks,  fire 207  212 

trespass 206  212 

National  forest  policy,  in  land  classification 250  238 

forests,  cost  of  replacement  as  basis  of  damages,  on 137  126 

Natural  resources,  value  of 9  5 

Nature  of  risks  in  forestry 198  208 

Non-agricultural  soils,  definition  of 232  228 

Normal  forest,  cost  of  producing  a 109  84 

definition  of 109  84 

profit  in  forestry 107  82 

Operating  costs,  future,  effect  on  stumpage  values 190  201 

Opportunity,  economic 27  16 

limitation  of 50  29 

Outlay 6  3 

classification  of,  in  accounts 21  13 

permanent,  in  forestry 93  71 

past,  independence  of  capital  value 68  44 

purpose  of 20  1 1 

temporary,  in  forestry 94  71 

and  income  accounts 21  12 

account,  general,  in  forestry 131  118 

relation  in  time  between 23  14 

Overhead  charges 25  16 

distribution  of,  in  lumbering  mixed  stands 180  188 

Overturn  methods  of  appraising  profits  in  lumbering 177  181 

Overrun 179  187 

Ownership 7  3 

Paper  pulp,  use  of  wood  for 189  200 

Parcels,  cost  accounts  by,  versus  entire  operation 181  193 

Partial  loss,  immature  timber,  damages 141  132 

Past  outlay  or  cost,  independence  of  capital  value 68  44 

Penalty,  taxes  paid  on  cancellation  of  classification 166  164 

Pennsylvania,  taxation  of  forests  in 166  161 

Per  cent,  current  annual  forest 129  114 

economic,  on  forest  investments 129  112 

of  slope  for  agricultural  soil 227  226 

values  taken  by  taxation,  Table  II 158  149 

mean  annual  forest 129  114 

Period  of  installation 23  14 

Permanent  improvements  and  equipment,  investment  in 97  73 

outlay  in  forestry 93  71 


INDEX  303 

ARTICLE  PAGE 

Perpetual  rentals,  explanation  of  meaning 86  64 

present,  expectation  or  capital  value  of 86  62 

Personal  factors  in  determination  of  agricultural  soil 230  227 

Personality,  influence  of,  upon  rate  of  interest 44  26 

Philosophy  of  accounts,  by  Charles  E.  Sprague 73  52 

Physical  risks,  definition  of 198  197 

fire 200  209 

fungous  diseases 203  211 

insects 202  211 

wind 201  210 

separation  of  timber  from  soil 133  122 

Pine  needles,  inflammability 200  210 

Potential  income 73  48 

Present  condition  of  forest,  effect  upon  methods  of  taxation 158  147 

value  of  future  sums 77  54 

perpetual  rentals . •  .  86  62 

temporary  annual  rentals 81  58 

intermittent  rentals 83  60 

Price  basis  in  appraisals 172  170 

changes  in  forest  products 188  197 

general  price  changes  affecting  stumpage  values 187  197 

levels,  changes  in  prices  of  forest  products 188  197 

Prices,  definition 3  2 

for  grades  of  lumber,  as  basis  of  stumpage  appraisals 172  171 

future,  and  values,  uncertainty  of 63  41 

of  finished  products 8  4 

raw  materials  and  natural  resources 9  5 

stumpage 169  167 

factors  determining 170  167 

Principles  underlying  appraisal  of  damages 133  120 

Private  measures  for  control  of  fire  risks 211  214 

versus  public  forestry,  profits  in 130  115 

Problem  of  the  balance  sheet 73  46 

interest,  the 36  20 

in  forest  taxation 167  146 

taxation  for  timber  lands 166  145 

Products,  improvement  in  quality  of 184  196 

tax 162  152 

Profit  and  loss  account,  form  for 73  50 

in  forestry 131  118 

accounts 21  12 

enterpriser's 39  23 

in  lumbering,  investment  basis  of 178  184 

Profits  as  a  per  cent  of  logging  and  milling  costs 177  182 

margin  between  sale  value  of  lumber,  and  costs 177  184 

sale  value  of  lumber 177  183 

annual 40  23 

anticipated,  on  young  timber 124  106 


304  INDEX 

ARTICLE  PAGE 

Profits,  continuous,  anticipation  of 126  107 

deferred 41  23 

definition  of 33  19 

economic 33  19 

expressed  as  a  ratio  of  income  to  capital 128  1 10 

expressed  in  soil  values 127  108 

formulae  for 246 

from  continuous  forest  production 126  107 

in  private  versus  public  forestry 130  115 

destructive  lumbering 122  105 

logging 175  179 

lumbering,  overturn  methods 177  181 

milling 174  177 

income  versus 42  24 

of  logging  contractors 177  182 

the  undertaking,  the 39  23 

on  a  stand  of  timber 123  106 

rate  of  interest  in  its  relation  to 121  104 

versus  carrying  charges  on  stumpage 181  191 

wages  versus 34  19 

Property,  definition  of 1  i 

tax,  forest 169  149 

general 164  144 

general,  forest  taxes  under 164  155 

on  value  of 161  142 

taxable  value  of 162  143 

values,  effect  of  taxes  on 163  143 

Proprietary  accounts 19  1 1 

in  forestry 91  69 

Proprietorship  in  balance  sheet 73  46 

Prospectus  or  forecast  in  accounting 73  51 

Protection,  expenses  for 100  74 

Protective  values,  damage  to 146  137 

Proximate  damages 133  121 

Public  measures  for  control  of  risks 210  213 

policy  in  regulating  private  forestry 130  116 

versus  private  forestry,  profits  in 130  115 

Punitive  damages 147  139 

Purchasers  of  land,  exploitation  of 234  229 

Quality  of  agricultural  soil 226  226 

products,  improvement  in 184  196 

timber,  estimation  of 223  222 

Railroad  assets,  valuation  of,  during  construction 57  36 

ties,  use  of  wood  for 189  200 

Rate  of  increase  in  stumpage  value 194  204 

interest,  the 38  22 


INDEX  305 

ARTICLE  PAGE 

Rate  of  interest,  as  affecting  damages 139  I3I 

earned 121  IOS 

effect  of,  upon  capital  value 66  42 

deferred  income  upon 48  28 

upon  accumulations  of  compound  interest 61  30 

in  forest  investments 51  -12 

forestry,  versus  risks 197  2o8 

its  relation  to  profits 121  104 

influences  determining  the 43  26 

Rates  of  interest,  in  forestry,  comparison  with  other  investments 53  33 

Ratio  of  income  or  earnings,  to  investments 89  66 

to  capital,  profits  expressed  as 128  no 

Raw  materials,  prices  of 9  5 

material,  stumpage  as  a  cost  of 176  181 

Reciprocal  values  in  forestry  and  agriculture 261  239 

Reconnaissance,  definition  of 66  35 

map 214  217 

Reform,  tax,  for  forest  property 166  160 

Regulation  of  capitalization 72  46 

'   private  forestry  by  public  measures 130  117 

Relative  importance  of  profits  in  private  versus  public  forestry 130  115 

Relation  of  rate  of  interest  to  profits 121  104 

Rental  value,  definition  of 62  40 

Rentals,  definition  of 76  53 

Replacement,  cost  of,  basis  of  damages 137  1 26 

Reports,  stumpage  appraisals 224  222 

Resistance  of  trees  to  wind 201  210 

Results  of  simple  and  compound  interest,  comparison  of 49  28 

Returns  on  capital 31  18 

Re-valuation  of  assets 73  48 

Revenue  from  which  to  meet  taxes,  sources  of 149  141 

Revision  of  stumpage  values  in  long  term  contracts 196  207 

Risk  and  expense  as  affecting  rate  of  interest 46  27 

Risks,  control  of  —  insurance 209  213 

effect  on  the  business  of  forest  production 212  214 

financial 208  212 

definition  of 198  208 

gauging  of 199  209 

in  forestry,  nature  of 198  208 

logging 176  179 

moral  —  trespass 206  212 

—  fire 207  212 

physical,  definition  of 198  208 

—  fire 200  209 

—  fungous  diseases 203  211 

—  injurious  fumes 206  212 

—  insects 202  211 

—  wind..,                                  201  210 


306  INDEX 

ARTICLE  PAGE 

Risks,  public  measures  for  control  of 210  213 

versus  rate  of  interest  in  forestry 197  208 

Roads  and  transportation  systems,  investment  in 98  73 

Salaries  versus  profits 34  19 

Sale  value 17  9 

as  a  basis  of  damages 138  128 

value 69  37 

effect  of  capital  value  upon 69  44 

of  agricultural  land 238  230 

forest  property 245  235 

forests Ill  86 

stump  lands 242  232 

stumpage 167  166 

Sales,  forced 17  10 

Savings  banks,  interest  rates  paid  by 53  33 

Scenery,  value  of 147  139 

Scientific  taxation,  combined  capital  tax  and  income  tax 154  163 

forest  land  tax 160  150 

property  tax 159  149 

income  or  products  tax 162  152 

Scope  of  field  appraisals  of  timber  stumpage 213  216 

Sedgwick  on  damages 133  121 

Sentimental  value  in  damages 133  121 

Separation  of  timber  from  soil,  physical 135  122 

value  of  timber  from  value  of  soil 136  123 

Services  or  labor  versus  investments 22  13 

Shingles,  use  of 189  199 

Silvicultural  operations,  cost  qf 99  74 

Simple  interest • 16  9 

comparison  of  results  with  compound  interest 49  28 

Single  trees,  damage  to 144  136 

Slash  disposal,  cost  of 100  74 

Slope,  per  cent,  for  agricultural  soil 227  226 

Soils,  agricultural,  definition  of 225  226 

Soil,  damage  to 143  135 

expectation  value  of 116  92 

quality  of 226  226 

rent 116  95 

as  a  cost  of  growing  timber 136  124 

deduction  from  damages 136  125 

theory  of 156  145 

versus  forest  rent,  comparison  of  taxes  on 161  151 

values,  profits  expressed  in 127  108 

Sources  of  revenue  from  which  to  meet  taxes 149  141 

Specific  accounts 19  n 

in  forestry,  forms  for 131  117 

balance  sheet  in  forestry 120  100 


INDEX  307 

ARTICLE  PAGE 

Specific  accounts,  costs 26  16 

Speculative  value 67  43 

Sprague,  Charles  E.,  philosophy  of  accounts 73  52 

Stand,  growth  in  volume  of 183  195 

improvement  in  quality  of  products 184  196 

Standard  log  rules 216  219 

of  value 2  i 

Standing  timber,  deterioration  of 186  196 

estimation  of 216  218 

investment  in 96  72 

State  forester,  power,  in  enforcing  tax  laws 166  164 

Strip  methods  of  timber  estimating 219  220 

Stump  lands,  cost  of  clearing 241  232 

sale  value  of 242  232 

land  versus  cleared  land 240  231 

Stumpage,  carrying  charges  on,  versus  profits 181  191 

appraisals,  future  local  supply  of  timber  as  affecting 193  204 

local  industries  and  markets 193  204 

reports 224  222 

as  a  capital  investment 176  180 

cost  of  raw  material 176  181 

prices 169  167 

factors  determining 170  167 

sale  value  of 168  166 

value,  appraisal  of 171  169 

rate  of  increase  in 194  204 

values,  definition  of 167  166 

for  different  species  in  mixed  stands 180  188 

formulae  for 248 

revision  of,  in  long  term  contracts 196  207 

Substitutes,  effect  of,  on  wood  prices 189  198 

Summary  of  elements  of  value  for  forest  land 243  233 

formulae  in  forest  valuation 243 

of  compound  interest 240 

Symbols,  definition  of 241 

Table  I  —  Comparison  of  Results  of  Simple  and  Compound  Interest. . .  61  30 

Table  II  —  Comparison  of  Results  of  Taxation  of  Capital  Values 158  148 

Table  III  —  Comparison  of  Sale  Value  with  Expectation  Value  of 

Even-aged  Stand 164  156 

Table  IV  —  Periods  within  which  Property  Tax  on  Timber  Becomes 

Equivalent  to  Tax  on  Soil  Value 166  159 

Table  V  —  Rate  of  Annual  Increase  in  Value  of  Stumpage 194  205 

Table  VI  —  Compound  Interest  Tables 249 

Table  VII  —  Logarithms  of  Numbers 265 

Tax,  general  property 154  J44 

on  income 15°  T4i 

reform  for  forest  property 166  160 


308  INDEX 

ARTICLE  PAGE 

Tax  on  value  of  property 151  142 

Taxable  value  of  property 152  143 

Taxation  for  timber  lands,  problem  of 165  145 

of  forest  land  bare  of  timber 166  161 

bearing  merchantable  timber 166  162 

property  in  Massachusetts 166  163 

Pennsylvania 166  161 

per  cent  of  values  taken  by,  for  forest  property 158  149 

scientific,  combined  capital  tax  and  income  tax 163  154 

forest  property  tax 159  149 

land  tax 160  150 

income  or  products  tax 162  152 

Taxes  as  an  expense 103  76 

based  on  value,  not  on  cost 161  151 

comparison  for  forests  of  different  age  classes,  Table  II 158  148 

of,  on  basis  of  forest  rent  versus  soil  rent 161  151 

sources  of  revenue  from  which  to  meet 149  141 

under  general  property  tax 164  155 

Telephone  installation,  cost  of 100  75 

Temporary  annual  rentals,  future  value  of 79  56 

present,  expectation  or  capital  value  of 81  58 

intermittent  rentals,  future  value  of 82  59 

present,  expectation  or  capital  value  of 83  60 

outlay  in  forestry 94  71 

Theory  of  forest  rent 156  146 

soil  rent 166  145 

Timber  as  an  agricultural  value 239  230 

bonds,  security  for 96  72 

cost  of  investments  in 106  79 

deterioration  of 185  196 

estimates,  closeness  of  utilization  as  affecting 217  219 

estimating,  correction  factors 222  221 

errors  in  methods 219  220 

field  methods  of 218  219 

quality  of  timber 223  222 

reports 224  222 

strip  methods 219  220 

use  of  forest  types  in 221  221 

estimation  of 216  218 

immature,  partial  loss,  damages 141  132 

total  loss,  damages 142  133 

lands,  problem  of  taxation  for 166  145 

merchantable,  definition  of 167  166 

damage  to 140  131 

reconnaissance;  the  map 214  217 

rights 96  72 

separate  from  land,  value  of 119  98 

standing,  investment  in 96  72 


INDEX  309 

ARTICLE  PAGE 

Time,  as  a  factor  controlling  stumpage  prices 170  169 

element  in  capital  value 64  42 

of,  in  values 11  6 

relation  in,  between  outlay  and  income 23  14 

Total  costs,  calculation  of,  in  growing  timber 106  77 

investment  includes  working  capital 24  15 

loss,  immature  timber,  damages 142  133 

Trading  and  profit  and  loss  account  in  forestry 131  118 

Transportation  costs,  effect  on  stumpage  prices 170  169 

effect  of  methods,  upon  logging  costs 175  178 

facilities,  future,  as  a  local  factor  in  stumpage  appraisals 190  202 

systems  and  roads,  investments  in 98  73 

Trees,  damage  to 144  136 

Trespass,  damage  as  result  of 140  131 

as  a  moral  risk 206  212 

Types,  forest,  in  timber  estimating 221  221 

Uncertainty  of  capital  value 67  43 

Undertaking,  profits  of  the 39  23 

Use  of  logarithms 78  55 

Uses  of  wood 189  199 

Utilization,  closeness  of 186  197 

as  affecting  timber  estimates 217  2 19 

Valuation  accounts 19  n 

versus  specific  accounts 64  35 

in  forestry 110  85 

of  railroad  assets  during  period  of  construction 67  36 

Value,  appraisal  of 60  38 

appraised 18  10 

capital,  definition  of 62  39 

uncertainty  of 67  43 

capitalized  income,  definition  of 62  40 

rental,  definition  of 62  40 

cost  as  a  basis  of 66  35 

essential  difference  between  cost  and 68  37 

expectation,  definition  of 62  39 

expenses  and  interest  versus 67  35 

future  income  as  a  basis  of 61  38 

income,  definition  of 62  40 

of  even-aged  forest  for  any  year 116  90 

finished  products 4  2 

a  forest  of  even  age  just  previous  to  cutting 114  89 

forests,  income  as  basis  of Ill  85 

forest  land,  elements  of 243  233 

property  for  continuous  forest  production 113  88 

destructive  lumbering 112  86 

soil...                       116  92 


310  INDEX 

ARTICLE  PAGE 

Value  of  growing  stock,  even-aged 119  98 

many-aged 119  99 

many-aged  forests  producing  irregular  income 118  97 

regular  income 117  96 

money 2  i 

fluctuating,  as  affecting  rate  of  interest 46  27 

property,  tax  on 151  142 

scenery 147  139 

soil,  separation  from  value  of  timber 136  123 

timber  separate  from  land 119  98 

young  timber  as  part  of  the  value  of  forest  soil 244  234 

rental,  definition  of 62  40 

sale 17  9 

as  a  basis  of : 59  37 

speculative 67  43 

standard  of 2  i 

stumpage,  definition  of 167  166 

appraisal  of 171  169 

taxable 152  143 

time  element  in  capital 64  42 

Values 4  2 

aesthetic 147  138 

formulas  for 244 

effect  of  taxes  on 153  143 

future,  uncertainty  of 63  41 

in  forestry  and  agriculture,  reciprocal 251  239 

of  stumpage  for  different  species  in  mixed  stands 180  188 

Volume  growth  of  stand 183  195 

Wages  versus  profits 34  19 

Water  supply,  dependence  of  agriculture  on 229  227 

Watersheds,  damage  to 146  137 

Wealth 1  i 

Wilful  trespass,  principle  of  damages  in 140  131 

Wind,  as  a  physical  risk 201  210 

Withdrawal  of  capital 73  49 

Wood  prices,  effect  of  substitutes  on 189  198 

Wood,  uses 189  199 

Woodlot,  effect  on  sale  value  of  farm 138  128 

Woodpeckers 202  211 

Woodworking  industries,  effect  on  local  stumpage  values 192  203 

Working  capital 24  15 

Yields  per  acre,  basis  of  damages 139  130 

Young  timber,  anticipated  profits  on 124  106 

value  of,  as  part  of  the  value  of  forest  soil 244  234 


UNIVERSITY  OF  CALIFORNIA  AT  LOS  ANGELES 

THE  UNIVERSITY  LIBRARY 
This  book  is  DUE  on  the  last  date  "tamped  Ivlo 


i  ii  111  ii  in  i  nun  ill  II 

A     001  138  292    6 


